Selena Romero - Assignment 6 - R Code - Summer 2020
Selena Romero
7/14/2020
Chapter 7 - Moving Beyond Linearity
Problem 6
In this exercise, you will further analyze the Wage data set considered throughout this chapter.
library(ISLR)
summary(Wage)## year age maritl race
## Min. :2003 Min. :18.00 1. Never Married: 648 1. White:2480
## 1st Qu.:2004 1st Qu.:33.75 2. Married :2074 2. Black: 293
## Median :2006 Median :42.00 3. Widowed : 19 3. Asian: 190
## Mean :2006 Mean :42.41 4. Divorced : 204 4. Other: 37
## 3rd Qu.:2008 3rd Qu.:51.00 5. Separated : 55
## Max. :2009 Max. :80.00
##
## education region jobclass
## 1. < HS Grad :268 2. Middle Atlantic :3000 1. Industrial :1544
## 2. HS Grad :971 1. New England : 0 2. Information:1456
## 3. Some College :650 3. East North Central: 0
## 4. College Grad :685 4. West North Central: 0
## 5. Advanced Degree:426 5. South Atlantic : 0
## 6. East South Central: 0
## (Other) : 0
## health health_ins logwage wage
## 1. <=Good : 858 1. Yes:2083 Min. :3.000 Min. : 20.09
## 2. >=Very Good:2142 2. No : 917 1st Qu.:4.447 1st Qu.: 85.38
## Median :4.653 Median :104.92
## Mean :4.654 Mean :111.70
## 3rd Qu.:4.857 3rd Qu.:128.68
## Max. :5.763 Max. :318.34
## str(Wage)## 'data.frame': 3000 obs. of 11 variables:
## $ year : int 2006 2004 2003 2003 2005 2008 2009 2008 2006 2004 ...
## $ age : int 18 24 45 43 50 54 44 30 41 52 ...
## $ maritl : Factor w/ 5 levels "1. Never Married",..: 1 1 2 2 4 2 2 1 1 2 ...
## $ race : Factor w/ 4 levels "1. White","2. Black",..: 1 1 1 3 1 1 4 3 2 1 ...
## $ education : Factor w/ 5 levels "1. < HS Grad",..: 1 4 3 4 2 4 3 3 3 2 ...
## $ region : Factor w/ 9 levels "1. New England",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ jobclass : Factor w/ 2 levels "1. Industrial",..: 1 2 1 2 2 2 1 2 2 2 ...
## $ health : Factor w/ 2 levels "1. <=Good","2. >=Very Good": 1 2 1 2 1 2 2 1 2 2 ...
## $ health_ins: Factor w/ 2 levels "1. Yes","2. No": 2 2 1 1 1 1 1 1 1 1 ...
## $ logwage : num 4.32 4.26 4.88 5.04 4.32 ...
## $ wage : num 75 70.5 131 154.7 75 ...- Perform polynomial regression to predict wage using age. Use cross-validation to select the optimal degree d for the polynomial. What degree was chosen, and how does this compare to the results of hypothesis testing using ANOVA? Make a plot of the resulting polynomial fit to the data.
Using K-Fold Cross Validation with K = 10 -
library(boot)
set.seed(1010)
cv.error <- rep(0, 5) # Initiate an empty vector to store computed Cross Validation Errors
for (i in 1:5) { # For-Loop to Increment from 1 to 5
wage.fit<-glm(wage~poly(age, i, raw = T), data=Wage) # Fit the Generalized Linear Regression Model
cv.error[i]<-cv.glm(Wage, wage.fit, K=10)$delta[1] # Calculate the Cross Validation Error
}
cv.error # Print Out the Resulting Cross Validation Error## [1] 1675.708 1599.987 1596.459 1595.367 1595.502plot(1:5, cv.error, xlab="Degree for Polynomial", ylab = "CV Error", type = "l")
d.min<-which.min(cv.error) # Finds Lowest CV Error
points(d.min, cv.error[d.min], col="red", cex=2, pch=20) # Plots Lowest CV Error
Using K-Fold Cross-Validation, the optimal degree for the Polynomial is 4 with the Cross Validation Error of 1595.367.
ANOVA Hypothesis Testing -
fit.1=lm(wage~age, data = Wage)
fit.2=lm(wage~poly(age,2, raw = T), data = Wage)
fit.3=lm(wage~poly(age,3, raw = T), data = Wage)
fit.4=lm(wage~poly(age,4, raw = T), data = Wage)
fit.5=lm(wage~poly(age,5, raw = T), data = Wage)
anova(fit.1,fit.2,fit.3,fit.4,fit.5)## Analysis of Variance Table
##
## Model 1: wage ~ age
## Model 2: wage ~ poly(age, 2, raw = T)
## Model 3: wage ~ poly(age, 3, raw = T)
## Model 4: wage ~ poly(age, 4, raw = T)
## Model 5: wage ~ poly(age, 5, raw = T)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 2998 5022216
## 2 2997 4793430 1 228786 143.5931 < 2.2e-16 ***
## 3 2996 4777674 1 15756 9.8888 0.001679 **
## 4 2995 4771604 1 6070 3.8098 0.051046 .
## 5 2994 4770322 1 1283 0.8050 0.369682
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1With the ANOVA Test, the Null Hypothesis (\(H_0\)) explains that a simple model is sufficient to explain the data. Whereas the Alternative Hypothesis (\(H_a\)) explains that a more complex model is required. In this case, the p-value comparing the linear Model 1 to the quadratic Model 2 is essentially zero, indicating that a linear fit is not sufficient. Similarly the p-value comparing the quadratic Model 2 to the cubic Model 3 is very low with a p-value of 0.001679, so this inidicates that the quadratic fit is also insufficient to explain the data. Looking at p-value comparing cubic Model 3 and quartic Model 4 is approximately 5.10% which will not pass this test with a cut-off at p-value = 0.05 - thus the quartic Model 4 is unnecessary. Lastly, with the large p-value comparing quartic Model 4 and quintic Model 5, explains that the higher-degree of 5 is definitely unnecessary. Hence, the cubic Model 3 is sufficient in explaining the data and provides a reasonable fit to the data.
Ploting the Two Polynomials selected by K-Folds Cross-Validation and ANOVA -
plot(wage~age, data=Wage, col="grey80", main="Polynomial Degree of 3 & 4 for Age Against Wage")
agelimit = range(Wage$age)
age.grid = seq(from = agelimit[1], to = agelimit[2])
wage.poly.3 = lm(wage~poly(age,3), data = Wage)
preds=predict(wage.poly.3, newdata = list(age = age.grid))
lines(age.grid, preds, col="royalblue1", lwd=2)
wage.poly.4 = lm(wage~poly(age,4), data = Wage)
preds2 = predict(wage.poly.4, newdata = list(age = age.grid))
lines(age.grid, preds2, col="indianred1", lwd=2)
The two Polynomials where d = 3 and d = 4 show similar movements along the data except when the age = 75 and on.
- Fit a step function to predict wage using age, and perform cross-validation to choose the optimal number of cuts. Make a plot of the fit obtained.
We will utilize K-Folds Cross-Validation to determine the optimal number of cuts for a step function -
set.seed(1010)
cut.cv.err = rep(NA, 10)
for (i in 2:10) { # For-Loop to Increment from 2 to 10 Cuts
Wage$age.cut=cut(Wage$age, i) # Cutspoints per i
fit.cut=glm(wage~age.cut, data=Wage) # Fit Generalized Linear Model
cut.cv.err[i]=cv.glm(Wage, fit.cut, K=10)$delta[1] # Caclulate the Cross Validation Error
}
cut.cv.err # Print Cross-Validation Error ## [1] NA 1734.170 1682.765 1636.465 1633.622 1624.730 1610.688 1602.017
## [9] 1611.424 1603.890plot(2:10, cut.cv.err[-1], main= "Selecting # of Cuts for Step Function", xlab = "Cuts", ylab="CV Error", type="l")
d.min=which.min(cut.cv.err)
points(which.min(cut.cv.err), cut.cv.err[which.min(cut.cv.err)], col="red", cex=2, pch=20)
With K-Folds Cross-Validation, the optimal # of Cuts selected is 8.
With Cuts = 8, I will fit the Step Function -
plot(wage~age, data = Wage, col = "grey80", main = "Step Function with 8 Cuts")
step.fit = glm(wage~cut(age,8), data = Wage)
step.preds = predict(step.fit, list(age = age.grid))
lines(age.grid, step.preds, col = "orchid4", lwd=2)
As described in the book, we use the Step Function in order to avoid imposing such a global structure to the data. In the graph above, you will see that the data is separated into 8 different bins to describe the trends with wage in relation to age. This function is typically used for data like this where the you are attempting to understand trends against several age groups.
Problem 10
This question relates to the College data set.
library(ISLR)
summary(College)## Private Apps Accept Enroll Top10perc
## No :212 Min. : 81 Min. : 72 Min. : 35 Min. : 1.00
## Yes:565 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242 1st Qu.:15.00
## Median : 1558 Median : 1110 Median : 434 Median :23.00
## Mean : 3002 Mean : 2019 Mean : 780 Mean :27.56
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902 3rd Qu.:35.00
## Max. :48094 Max. :26330 Max. :6392 Max. :96.00
## Top25perc F.Undergrad P.Undergrad Outstate
## Min. : 9.0 Min. : 139 Min. : 1.0 Min. : 2340
## 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0 1st Qu.: 7320
## Median : 54.0 Median : 1707 Median : 353.0 Median : 9990
## Mean : 55.8 Mean : 3700 Mean : 855.3 Mean :10441
## 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0 3rd Qu.:12925
## Max. :100.0 Max. :31643 Max. :21836.0 Max. :21700
## Room.Board Books Personal PhD
## Min. :1780 Min. : 96.0 Min. : 250 Min. : 8.00
## 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850 1st Qu.: 62.00
## Median :4200 Median : 500.0 Median :1200 Median : 75.00
## Mean :4358 Mean : 549.4 Mean :1341 Mean : 72.66
## 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700 3rd Qu.: 85.00
## Max. :8124 Max. :2340.0 Max. :6800 Max. :103.00
## Terminal S.F.Ratio perc.alumni Expend
## Min. : 24.0 Min. : 2.50 Min. : 0.00 Min. : 3186
## 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00 1st Qu.: 6751
## Median : 82.0 Median :13.60 Median :21.00 Median : 8377
## Mean : 79.7 Mean :14.09 Mean :22.74 Mean : 9660
## 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00 3rd Qu.:10830
## Max. :100.0 Max. :39.80 Max. :64.00 Max. :56233
## Grad.Rate
## Min. : 10.00
## 1st Qu.: 53.00
## Median : 65.00
## Mean : 65.46
## 3rd Qu.: 78.00
## Max. :118.00str(College)## 'data.frame': 777 obs. of 18 variables:
## $ Private : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 2 2 2 2 2 ...
## $ Apps : num 1660 2186 1428 417 193 ...
## $ Accept : num 1232 1924 1097 349 146 ...
## $ Enroll : num 721 512 336 137 55 158 103 489 227 172 ...
## $ Top10perc : num 23 16 22 60 16 38 17 37 30 21 ...
## $ Top25perc : num 52 29 50 89 44 62 45 68 63 44 ...
## $ F.Undergrad: num 2885 2683 1036 510 249 ...
## $ P.Undergrad: num 537 1227 99 63 869 ...
## $ Outstate : num 7440 12280 11250 12960 7560 ...
## $ Room.Board : num 3300 6450 3750 5450 4120 ...
## $ Books : num 450 750 400 450 800 500 500 450 300 660 ...
## $ Personal : num 2200 1500 1165 875 1500 ...
## $ PhD : num 70 29 53 92 76 67 90 89 79 40 ...
## $ Terminal : num 78 30 66 97 72 73 93 100 84 41 ...
## $ S.F.Ratio : num 18.1 12.2 12.9 7.7 11.9 9.4 11.5 13.7 11.3 11.5 ...
## $ perc.alumni: num 12 16 30 37 2 11 26 37 23 15 ...
## $ Expend : num 7041 10527 8735 19016 10922 ...
## $ Grad.Rate : num 60 56 54 59 15 55 63 73 80 52 ...attach(College)- Split the data into a training set and a test set. Using out-of-state tuition as the response and the other variables as the predictors, perform forward stepwise selection on the training set in order to identify a satisfactory model that uses just a subset of the predictors.
Splitting Data into Training and Testing Data -
library(caret)## Loading required package: lattice##
## Attaching package: 'lattice'## The following object is masked from 'package:boot':
##
## melanoma## Loading required package: ggplot2library(leaps)
library(tidyr)
library(modelr)
set.seed(5432)
train.index <- createDataPartition(College$Outstate, p = 0.75, list = FALSE)
College.train <- College[train.index,]
College.test <- College[-train.index,]Forward Stepwise Selection on Training Data -
dummy.matrix <- model.matrix(Outstate ~., data = College.train)
College.fwd.selection <- regsubsets(x = dummy.matrix, y = College.train$Outstate, nvmax = 17, method = "forward")## Reordering variables and trying again:fwd.summary <- summary(College.fwd.selection)
fwd.summary## Subset selection object
## 18 Variables (and intercept)
## Forced in Forced out
## PrivateYes FALSE FALSE
## Apps FALSE FALSE
## Accept FALSE FALSE
## Enroll FALSE FALSE
## Top10perc FALSE FALSE
## Top25perc FALSE FALSE
## F.Undergrad FALSE FALSE
## P.Undergrad FALSE FALSE
## Room.Board FALSE FALSE
## Books FALSE FALSE
## Personal FALSE FALSE
## PhD FALSE FALSE
## Terminal FALSE FALSE
## S.F.Ratio FALSE FALSE
## perc.alumni FALSE FALSE
## Expend FALSE FALSE
## Grad.Rate FALSE FALSE
## (Intercept) FALSE FALSE
## 1 subsets of each size up to 17
## Selection Algorithm: forward
## (Intercept) PrivateYes Apps Accept Enroll Top10perc Top25perc
## 1 ( 1 ) " " " " " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " " " " " "
## 4 ( 1 ) " " "*" " " " " " " " " " "
## 5 ( 1 ) " " "*" " " " " " " " " " "
## 6 ( 1 ) " " "*" " " " " " " " " " "
## 7 ( 1 ) " " "*" " " " " " " " " " "
## 8 ( 1 ) " " "*" " " " " " " " " " "
## 9 ( 1 ) " " "*" " " "*" " " " " " "
## 10 ( 1 ) " " "*" " " "*" " " " " " "
## 11 ( 1 ) " " "*" "*" "*" " " " " " "
## 12 ( 1 ) " " "*" "*" "*" " " "*" " "
## 13 ( 1 ) " " "*" "*" "*" " " "*" " "
## 14 ( 1 ) " " "*" "*" "*" " " "*" " "
## 15 ( 1 ) " " "*" "*" "*" "*" "*" " "
## 16 ( 1 ) " " "*" "*" "*" "*" "*" "*"
## 17 ( 1 ) " " "*" "*" "*" "*" "*" "*"
## F.Undergrad P.Undergrad Room.Board Books Personal PhD Terminal
## 1 ( 1 ) " " " " "*" " " " " " " " "
## 2 ( 1 ) " " " " "*" " " " " " " " "
## 3 ( 1 ) " " " " "*" " " " " " " " "
## 4 ( 1 ) " " " " "*" " " " " " " " "
## 5 ( 1 ) " " " " "*" " " " " " " "*"
## 6 ( 1 ) " " " " "*" " " " " " " "*"
## 7 ( 1 ) " " " " "*" " " "*" " " "*"
## 8 ( 1 ) " " " " "*" " " "*" " " "*"
## 9 ( 1 ) " " " " "*" " " "*" " " "*"
## 10 ( 1 ) "*" " " "*" " " "*" " " "*"
## 11 ( 1 ) "*" " " "*" " " "*" " " "*"
## 12 ( 1 ) "*" " " "*" " " "*" " " "*"
## 13 ( 1 ) "*" " " "*" " " "*" "*" "*"
## 14 ( 1 ) "*" "*" "*" " " "*" "*" "*"
## 15 ( 1 ) "*" "*" "*" " " "*" "*" "*"
## 16 ( 1 ) "*" "*" "*" " " "*" "*" "*"
## 17 ( 1 ) "*" "*" "*" "*" "*" "*" "*"
## S.F.Ratio perc.alumni Expend Grad.Rate
## 1 ( 1 ) " " " " " " " "
## 2 ( 1 ) " " "*" " " " "
## 3 ( 1 ) " " "*" "*" " "
## 4 ( 1 ) " " "*" "*" " "
## 5 ( 1 ) " " "*" "*" " "
## 6 ( 1 ) " " "*" "*" "*"
## 7 ( 1 ) " " "*" "*" "*"
## 8 ( 1 ) "*" "*" "*" "*"
## 9 ( 1 ) "*" "*" "*" "*"
## 10 ( 1 ) "*" "*" "*" "*"
## 11 ( 1 ) "*" "*" "*" "*"
## 12 ( 1 ) "*" "*" "*" "*"
## 13 ( 1 ) "*" "*" "*" "*"
## 14 ( 1 ) "*" "*" "*" "*"
## 15 ( 1 ) "*" "*" "*" "*"
## 16 ( 1 ) "*" "*" "*" "*"
## 17 ( 1 ) "*" "*" "*" "*"par(mfrow=c(2,2))
plot(fwd.summary$adjr2, pch=19, main="Adjusted R2", xlab="Number of Variables Used", ylab="Adjusted R2 Values")
plot(fwd.summary$bic, pch=19, main="BIC", xlab="Number of Variables Used", ylab="BIC")
RMSE=sqrt(fwd.summary$rss/nrow(College.train))
plot(RMSE, pch=19, main="RMSE", xlab="Number of Variables Used", ylab ="RMSE")
plot(fwd.summary$cp, pch=19, main="CP", xlab="Number of Variables Used", ylab="Cp")
BIC.min = which.min(fwd.summary$bic)
RMSE.min = which.min(RMSE)
AdjR2.max = which.max(fwd.summary$adjr2)
Cp.min = which.min(fwd.summary$cp)
BIC.min## [1] 12RMSE.min## [1] 17AdjR2.max## [1] 12Cp.min## [1] 12Most of the measures for Model Fitness shows that 12 Variables should be used based on Forward Selection as 12 variables produces the lowest BIC and Cp but highest AdjR2. The variables to be included in the Forward Stepwise Model are: perc.alumni, Expend, Grad.Rate, Terminal, S.F.Ratio, Personal, F.Undergrad, Room.Board, PrivateYes, Apps, Accept, and Top10perc.
coef(College.fwd.selection, id = 12)## (Intercept) Apps Accept Enroll Top25perc
## 1.620107e+03 -3.828618e-01 1.140728e+00 -2.170808e+00 1.862147e+01
## P.Undergrad Books PhD S.F.Ratio perc.alumni
## 3.738807e-04 1.081745e-01 2.549982e+01 -9.263174e+01 5.889231e+01
## Expend Grad.Rate (Intercept)
## 2.879859e-01 5.499454e+01 0.000000e+00- Fit a GAM on the training data, using out-of-state tuition as the response and the features selected in the previous step as the predictors. Plot the results, and explain your findings.
For fitting the GAM Model, I want to first find the most appropriate degrees of freedom to allow. To find the appropriate degrees of freedom, I will utilize K-Folds Cross-Validation.
coefs <- names(coef(College.fwd.selection, id = 12))
coefs <- coefs[-grep('Intercept', coefs)]
College.gam <- train(x = College.train[,coefs], y = College.train$Outstate,
method = 'gamSpline',
trControl = trainControl(method = 'cv', number = 10),
tuneGrid = expand.grid(df = 1:10))
plot(College.gam)
The above plot shows that the optimal Degrees of Freedom chosen by K-Folds Cross-Validation where K = 10 is d = 3.
postResample(predict(College.gam, College.train), College.train$Outstate)## RMSE Rsquared MAE
## 1930.8793643 0.7728723 1519.8242102The GAM Model with d = 3 achieves a Training R-Squared of 0.7728723 or 77.287% which means that 77.287% of the variance in Outstate can be explained by the subset of 12 predictor variables selected by Cross-Validation. Additionally, this GAM Model achieves a RMSE of 1930.8793.
- Evaluate the model obtained on the test set, and explain the results obtained.
postResample(predict(College.gam, College.test), College.test$Outstate)## RMSE Rsquared MAE
## 2043.0852754 0.7308196 1581.7833109On the Test Data Set, the GAM achieves a slightly lower R-Squared and higher RMSE. This is okay considering that model will always perform best on the training data.
- For which variables, if any, is there evidence of a non-linear relationship with the response?
summary(College.gam)##
## Call: (function (formula, family = gaussian, data, weights, subset,
## na.action, start = NULL, etastart, mustart, control = gam.control(...),
## model = TRUE, method = "glm.fit", x = FALSE, y = TRUE, ...)
## {
## call <- match.call()
## if (is.character(family))
## family <- get(family, mode = "function", envir = parent.frame())
## if (is.function(family))
## family <- family()
## if (is.null(family$family)) {
## print(family)
## stop("`family' not recognized")
## }
## if (missing(data))
## data <- environment(formula)
## mf <- match.call(expand.dots = FALSE)
## m <- match(c("formula", "data", "subset", "weights", "etastart",
## "mustart", "offset"), names(mf), 0L)
## mf <- mf[c(1L, m)]
## mf$na.action = quote(na.pass)
## mf$drop.unused.levels <- TRUE
## mf[[1L]] <- quote(stats::model.frame)
## gam.slist <- gam.smoothers()$slist
## mt <- if (missing(data))
## terms(formula, gam.slist)
## else terms(formula, gam.slist, data = data)
## mf$formula <- mt
## mf <- eval(mf, parent.frame())
## if (missing(na.action)) {
## naa = getOption("na.action", "na.fail")
## na.action = get(naa)
## }
## mf = na.action(mf)
## mt = attributes(mf)[["terms"]]
## switch(method, model.frame = return(mf), glm.fit = 1, glm.fit.null = 1,
## stop("invalid `method': ", method))
## Y <- model.response(mf, "any")
## X <- if (!is.empty.model(mt))
## model.matrix(mt, mf, contrasts)
## else matrix(, NROW(Y), 0)
## weights <- model.weights(mf)
## offset <- model.offset(mf)
## if (!is.null(weights) && any(weights < 0))
## stop("Negative wts not allowed")
## if (!is.null(offset) && length(offset) != NROW(Y))
## stop("Number of offsets is ", length(offset), ", should equal ",
## NROW(Y), " (number of observations)")
## mustart <- model.extract(mf, "mustart")
## etastart <- model.extract(mf, "etastart")
## fit <- gam.fit(x = X, y = Y, smooth.frame = mf, weights = weights,
## start = start, etastart = etastart, mustart = mustart,
## offset = offset, family = family, control = control)
## if (length(offset) && attr(mt, "intercept") > 0) {
## fit$null.dev <- glm.fit(x = X[, "(Intercept)", drop = FALSE],
## y = Y, weights = weights, offset = offset, family = family,
## control = control[c("epsilon", "maxit", "trace")],
## intercept = TRUE)$deviance
## }
## if (model)
## fit$model <- mf
## fit$na.action <- attr(mf, "na.action")
## if (x)
## fit$x <- X
## if (!y)
## fit$y <- NULL
## fit <- c(fit, list(call = call, formula = formula, terms = mt,
## data = data, offset = offset, control = control, method = method,
## contrasts = attr(X, "contrasts"), xlevels = .getXlevels(mt,
## mf)))
## class(fit) <- c("Gam", "glm", "lm")
## if (!is.null(fit$df.residual) && !(fit$df.residual > 0))
## warning("Residual degrees of freedom are negative or zero. This occurs when the sum of the parametric and nonparametric degrees of freedom exceeds the number of observations. The model is probably too complex for the amount of data available.")
## fit
## })(formula = .outcome ~ s(perc.alumni, df = 3) + s(PhD, df = 3) +
## s(Grad.Rate, df = 3) + s(Top25perc, df = 3) + s(Books, df = 3) +
## s(S.F.Ratio, df = 3) + s(P.Undergrad, df = 3) + s(Enroll,
## df = 3) + s(Accept, df = 3) + s(Apps, df = 3) + s(Expend,
## df = 3), family = function (link = "identity")
## {
## linktemp <- substitute(link)
## if (!is.character(linktemp))
## linktemp <- deparse(linktemp)
## okLinks <- c("inverse", "log", "identity")
## if (linktemp %in% okLinks)
## stats <- make.link(linktemp)
## else if (is.character(link)) {
## stats <- make.link(link)
## linktemp <- link
## }
## else {
## if (inherits(link, "link-glm")) {
## stats <- link
## if (!is.null(stats$name))
## linktemp <- stats$name
## }
## else {
## stop(gettextf("link \"%s\" not available for gaussian family; available links are %s",
## linktemp, paste(sQuote(okLinks), collapse = ", ")),
## domain = NA)
## }
## }
## structure(list(family = "gaussian", link = linktemp, linkfun = stats$linkfun,
## linkinv = stats$linkinv, variance = function(mu) rep.int(1,
## length(mu)), dev.resids = function(y, mu, wt) wt *
## ((y - mu)^2), aic = function(y, n, mu, wt, dev) {
## nobs <- length(y)
## nobs * (log(dev/nobs * 2 * pi) + 1) + 2 - sum(log(wt))
## }, mu.eta = stats$mu.eta, initialize = expression({
## n <- rep.int(1, nobs)
## if (is.null(etastart) && is.null(start) && is.null(mustart) &&
## ((family$link == "inverse" && any(y == 0)) ||
## (family$link == "log" && any(y <= 0)))) stop("cannot find valid starting values: please specify some")
## mustart <- y
## }), validmu = function(mu) TRUE, valideta = stats$valideta),
## class = "family")
## }, data = structure(list(Apps = c(1660, 2186, 1428, 417, 193,
## 353, 1899, 582, 1732, 2652, 1267, 494, 1420, 4302, 1216, 1130,
## 3540, 713, 619, 12809, 662, 1879, 761, 948, 627, 602, 1690, 261,
## 2496, 990, 6075, 807, 632, 1320, 632, 519, 3466, 878, 202, 1646,
## 805, 500, 6773, 377, 692, 20192, 3356, 9251, 3767, 4186, 367,
## 1436, 392, 7365, 1465, 6548, 2362, 599, 1011, 563, 7811, 4540,
## 1784, 848, 2853, 1747, 100, 8728, 1160, 1096, 1616, 3847, 776,
## 1307, 369, 495, 1283, 4158, 2785, 174, 1013, 959, 342, 81, 880,
## 883, 1196, 1860, 2887, 2174, 689, 1006, 604, 2848, 4856, 1432,
## 4772, 798, 938, 444, 983, 546, 141, 672, 2994, 7117, 2100, 9478,
## 314, 737, 6756, 281, 232, 528, 3035, 440, 2967, 995, 866, 504,
## 585, 2373, 571, 967, 2762, 1994, 3014, 434, 1998, 793, 604, 1011,
## 2153, 700, 13789, 9274, 3330, 2172, 5597, 486, 1422, 2417, 245,
## 3624, 765, 659, 560, 1455, 1339, 1415, 1947, 3306, 291, 1801,
## 553, 804, 5187, 895, 346, 2161, 2464, 1110, 668, 727, 11115,
## 7837, 3793, 348, 3596, 633, 674, 440, 548, 5165, 608, 510, 2491,
## 1202, 3140, 1006, 817, 1006, 467, 1721, 2083, 13865, 1377, 817,
## 823, 920, 922, 7428, 602, 699, 1712, 608, 600, 607, 894, 8681,
## 3050, 268, 735, 4892, 8427, 7259, 11223, 472, 605, 2421, 8474,
## 313, 1005, 5880, 589, 2212, 1456, 355, 361, 2929, 4010, 544,
## 979, 497, 831, 1166, 1386, 6397, 979, 244, 477, 2774, 1154, 787,
## 1660, 810, 1561, 3570, 2747, 1641, 2013, 5996, 2397, 4076, 1891,
## 3579, 1549, 1756, 535, 2939, 740, 874, 1004, 2432, 962, 3073,
## 824, 4731, 499, 478, 941, 1464, 549, 1107, 6411, 1002, 578, 420,
## 2286, 1557, 1981, 1584, 1742, 9239, 6011, 610, 905, 1217, 594,
## 4255, 480, 1310, 601, 2707, 572, 263, 2442, 3708, 586, 882, 1800,
## 279, 368, 325, 1321, 657, 1310, 2519, 2225, 513, 947, 1879, 787,
## 13594, 872, 2220, 1563, 4809, 10634, 1127, 2968, 6040, 11901,
## 5891, 10706, 2729, 616, 12289, 1743, 4778, 2324, 792, 2936, 11023,
## 2190, 758, 776, 4522, 1496, 910, 2308, 8256, 1603, 940, 943,
## 944, 3821, 1538, 692, 404, 1133, 809, 875, 1132, 2405, 1082,
## 13218, 5139, 1025, 3712, 5702, 2088, 1771, 696, 1966, 4996, 3586,
## 587, 484, 2227, 935, 560, 3304, 1777, 434, 48094, 3366, 2307,
## 2095, 1046, 920, 833, 3294, 876, 2248, 700, 335, 1680, 9402,
## 4019, 584, 855, 1183, 4576, 5818, 1003, 1016, 437, 2925, 2807,
## 818, 2540, 4301, 1093, 6118, 1047, 213, 1244, 283, 3713, 372,
## 1489, 1368, 2753, 191, 2643, 1340, 1243, 1334, 651, 861, 450,
## 1557, 1768, 4019, 3646, 13528, 14463, 12512, 7294, 5318, 7888,
## 4877, 8399, 5549, 3150, 2119, 2096, 462, 257, 4414, 1769, 232,
## 14474, 4095, 497, 4345, 845, 759, 5042, 3058, 247, 7033, 626,
## 2267, 3495, 1797, 19873, 15698, 6986, 6348, 6855, 9735, 681,
## 14446, 2974, 927, 576, 2096, 12445, 11220, 5081, 3580, 14939,
## 8579, 441, 461, 14292, 14438, 3347, 19152, 4192, 1458, 11054,
## 3844, 6574, 1618, 452, 1351, 1209, 9750, 1757, 14596, 5191, 6071,
## 2777, 1800, 4418, 5530, 7700, 4743, 8631, 12394, 1758, 4044,
## 9643, 5892, 8766, 2306, 285, 848, 7693, 7589, 12229, 2379, 2850,
## 7473, 3281, 14752, 4217, 974, 2459, 1712, 5095, 7663, 15849,
## 12749, 1558, 2593, 910, 4400, 14901, 5244, 2029, 663, 1399, 325,
## 2075, 7791, 7759, 2996, 15712, 1847, 647, 1465, 800, 1416, 5661,
## 1092, 440, 1231, 1305, 3315, 1209, 6540, 7654, 1373, 1190, 280,
## 665, 1480, 4772, 6502, 1164, 1566, 3224, 1205, 9167, 1650, 2702,
## 5548, 3100, 662, 950, 1432, 1738, 903, 1861, 1681, 1121, 2139,
## 1631, 1658, 469, 167, 3325, 2320, 152, 2768, 2197, 1959, 2097,
## 10705, 2989), Accept = c(1232, 1924, 1097, 349, 146, 340, 1720,
## 498, 1425, 1900, 1080, 313, 1093, 992, 908, 704, 2001, 661, 516,
## 10308, 513, 1658, 725, 798, 556, 483, 1366, 192, 1402, 784, 5349,
## 707, 494, 923, 620, 327, 2330, 816, 184, 1150, 588, 336, 3028,
## 358, 514, 13007, 1019, 7333, 3414, 2743, 274, 1228, 351, 5402,
## 810, 3813, 2037, 494, 604, 247, 3817, 3294, 1512, 587, 2193,
## 1382, 90, 5201, 991, 951, 1427, 3433, 607, 1090, 312, 434, 1113,
## 2532, 2011, 146, 888, 771, 254, 72, 520, 766, 697, 767, 2059,
## 1953, 561, 742, 452, 1319, 2492, 888, 3140, 620, 864, 359, 664,
## 447, 118, 596, 1691, 3106, 1883, 6312, 158, 614, 1930, 266, 216,
## 403, 1546, 407, 2836, 789, 619, 482, 508, 956, 461, 945, 2279,
## 1656, 2539, 412, 1376, 709, 562, 829, 1580, 650, 3893, 6362,
## 2730, 1493, 4253, 440, 1109, 1843, 208, 2786, 646, 557, 454,
## 1064, 1107, 714, 1580, 2079, 245, 1655, 452, 632, 4471, 548,
## 274, 1951, 1908, 930, 534, 693, 2881, 4527, 2341, 281, 2466,
## 468, 565, 396, 428, 3887, 494, 387, 1110, 1054, 1783, 825, 644,
## 837, 424, 1068, 1725, 2165, 572, 708, 721, 745, 729, 5860, 498,
## 565, 1483, 520, 197, 558, 787, 6695, 1342, 253, 423, 3530, 7424,
## 5526, 5285, 410, 405, 2109, 3446, 228, 859, 4075, 575, 1538,
## 1053, 300, 321, 1834, 2402, 399, 638, 452, 538, 1009, 1060, 4304,
## 743, 198, 417, 2092, 1050, 562, 1091, 484, 1188, 2215, 1870,
## 1283, 1053, 4993, 2144, 3137, 1698, 2959, 1392, 1500, 502, 1496,
## 558, 758, 802, 1730, 750, 2672, 670, 3171, 441, 327, 772, 888,
## 397, 859, 2140, 555, 411, 293, 1668, 1074, 1541, 1456, 1382,
## 7788, 3075, 461, 834, 1088, 385, 3277, 405, 983, 503, 1881, 544,
## 223, 2164, 1678, 533, 730, 1314, 276, 317, 284, 1159, 537, 1086,
## 1836, 1910, 347, 798, 1216, 601, 7244, 722, 1796, 1005, 3089,
## 7064, 884, 2297, 4577, 8492, 4931, 7219, 2535, 514, 5200, 1625,
## 2767, 1319, 649, 2342, 8298, 1700, 681, 765, 3913, 1205, 773,
## 1336, 3750, 1392, 668, 849, 774, 2037, 1259, 576, 400, 630, 687,
## 744, 847, 2234, 832, 2042, 3346, 707, 2153, 4894, 957, 1325,
## 616, 1436, 4165, 2424, 501, 386, 1790, 858, 392, 2804, 1151,
## 321, 26330, 1752, 1896, 1553, 824, 684, 682, 2855, 802, 1673,
## 595, 284, 1395, 7020, 2779, 413, 632, 1016, 3565, 3281, 782,
## 872, 400, 1598, 2589, 700, 2195, 3455, 1093, 5254, 938, 155,
## 912, 201, 1237, 362, 1313, 1064, 1820, 165, 1611, 695, 1020,
## 1243, 581, 609, 405, 1227, 1249, 1579, 2300, 9198, 6166, 6969,
## 3564, 3515, 3519, 2798, 3609, 3583, 2289, 1264, 1512, 402, 183,
## 1500, 1092, 182, 10519, 3079, 423, 3245, 734, 729, 2312, 1798,
## 189, 5125, 372, 1827, 1712, 1260, 8252, 10775, 2959, 2999, 5553,
## 7187, 588, 10516, 2001, 731, 558, 1626, 8836, 7871, 4040, 2603,
## 11652, 5561, 369, 381, 10315, 12414, 2597, 12940, 3126, 874,
## 6397, 3383, 4637, 1141, 331, 892, 750, 7640, 979, 5985, 4134,
## 3856, 2249, 1253, 2737, 4007, 3700, 3970, 6732, 5232, 1485, 2826,
## 7751, 2718, 5498, 1721, 280, 560, 5815, 4676, 8498, 2133, 2044,
## 5372, 2559, 9572, 3100, 704, 1997, 1557, 4491, 6008, 5384, 7025,
## 1254, 1966, 910, 3719, 10932, 3782, 1516, 452, 1026, 260, 1727,
## 4690, 5588, 2440, 11719, 1610, 518, 1006, 623, 1015, 2392, 890,
## 311, 1074, 1100, 1096, 942, 5839, 5259, 1373, 978, 143, 462,
## 1257, 1973, 3539, 1062, 1400, 2519, 984, 7191, 1471, 1623, 3563,
## 2150, 553, 713, 920, 1373, 755, 998, 1069, 926, 1492, 1431, 1327,
## 435, 130, 2047, 1805, 128, 2314, 1515, 1805, 1915, 2453, 1855
## ), Enroll = c(721, 512, 336, 137, 55, 103, 489, 172, 472, 484,
## 385, 157, 220, 418, 423, 322, 1016, 252, 219, 3761, 257, 497,
## 306, 295, 172, 206, 662, 111, 531, 279, 2367, 308, 129, 284,
## 222, 114, 640, 200, 122, 542, 287, 156, 1025, 181, 209, 3810,
## 418, 3076, 1061, 740, 158, 1202, 155, 4615, 313, 862, 700, 224,
## 213, 247, 1650, 1483, 913, 298, 753, 449, 35, 1191, 352, 464,
## 434, 527, 198, 616, 90, 210, 401, 902, 1007, 88, 288, 351, 126,
## 51, 224, 428, 499, 227, 457, 557, 250, 275, 295, 456, 727, 317,
## 1265, 238, 511, 122, 249, 189, 55, 278, 659, 1217, 553, 2194,
## 132, 242, 871, 139, 106, 186, 438, 149, 876, 398, 157, 185, 153,
## 452, 174, 459, 533, 495, 487, 319, 651, 244, 328, 410, 321, 314,
## 1583, 2435, 1303, 564, 1565, 227, 366, 426, 125, 858, 226, 167,
## 113, 452, 336, 338, 523, 1071, 126, 819, 228, 281, 446, 314,
## 146, 685, 678, 332, 237, 286, 1390, 2276, 1238, 127, 575, 284,
## 282, 221, 167, 1561, 176, 194, 573, 326, 454, 328, 307, 317,
## 350, 806, 430, 1606, 178, 262, 274, 347, 244, 1349, 215, 176,
## 624, 127, 124, 269, 262, 2408, 471, 103, 366, 913, 3441, 1368,
## 2082, 262, 284, 820, 911, 137, 298, 2833, 148, 408, 381, 142,
## 185, 622, 572, 177, 271, 231, 224, 510, 320, 1092, 259, 82, 204,
## 482, 395, 363, 326, 356, 458, 651, 724, 527, 212, 3079, 1525,
## 738, 719, 868, 587, 366, 223, 452, 177, 428, 239, 563, 212, 1547,
## 337, 830, 199, 117, 214, 176, 169, 323, 1078, 119, 187, 93, 564,
## 397, 514, 891, 607, 3290, 960, 189, 319, 496, 307, 1609, 380,
## 316, 204, 478, 320, 103, 1189, 722, 239, 330, 526, 126, 159,
## 95, 328, 113, 458, 462, 1190, 279, 266, 483, 233, 2505, 154,
## 467, 240, 1429, 3176, 308, 1610, 1620, 2517, 1973, 2397, 1257,
## 385, 1902, 626, 678, 370, 186, 669, 3183, 458, 484, 351, 2181,
## 428, 450, 295, 1522, 504, 385, 288, 440, 680, 468, 174, 169,
## 220, 428, 207, 302, 1061, 302, 1153, 973, 297, 806, 1742, 362,
## 306, 169, 327, 936, 730, 211, 141, 437, 345, 270, 679, 382, 141,
## 4520, 232, 509, 514, 284, 225, 217, 956, 367, 745, 278, 132,
## 691, 2151, 888, 131, 139, 411, 1000, 1116, 295, 300, 211, 632,
## 1701, 447, 994, 1166, 642, 3204, 511, 75, 352, 97, 443, 181,
## 375, 354, 505, 63, 465, 285, 414, 568, 243, 215, 194, 489, 380,
## 710, 585, 1843, 1757, 1724, 904, 1025, 1036, 814, 656, 853, 650,
## 390, 465, 146, 109, 335, 437, 99, 6392, 1195, 215, 2604, 254,
## 244, 944, 478, 100, 1223, 145, 611, 528, 938, 3215, 2478, 1918,
## 922, 2408, 2064, 246, 3252, 580, 415, 137, 694, 3623, 3320, 1194,
## 1627, 5705, 3681, 172, 235, 3409, 3816, 1006, 4893, 1656, 588,
## 3524, 1669, 2940, 479, 269, 570, 265, 2529, 394, 3331, 1500,
## 1449, 1652, 560, 2049, 1697, 1906, 2233, 2546, 2464, 419, 688,
## 1968, 756, 1243, 538, 208, 377, 2328, 1876, 2477, 1292, 1046,
## 3013, 1448, 5329, 1686, 290, 582, 696, 2400, 1735, 2678, 3343,
## 472, 1030, 342, 1472, 4631, 1930, 1073, 192, 308, 86, 520, 1499,
## 1477, 704, 4277, 453, 271, 188, 256, 417, 903, 477, 112, 345,
## 334, 425, 214, 2440, 1254, 724, 324, 79, 226, 452, 712, 1372,
## 478, 483, 1057, 278, 2738, 409, 604, 1549, 825, 184, 351, 548,
## 417, 213, 359, 344, 372, 502, 434, 395, 227, 46, 1301, 769, 75,
## 682, 543, 695, 695, 1317, 691), Top25perc = c(52, 29, 50, 89,
## 44, 45, 68, 44, 75, 77, 73, 46, 22, 96, 40, 23, 54, 44, 51, 49,
## 30, 69, 58, 74, 40, 47, 61, 36, 95, 45, 66, 63, 36, 54, 24, 53,
## 60, 41, 42, 30, 88, 55, 55, 30, 50, 80, 100, 45, 58, 77, 41,
## 26, 44, 82, 95, 85, 68, 28, 42, 52, 73, 60, 56, 55, 34, 66, 52,
## 89, 55, 62, 43, 35, 58, 55, 46, 55, 65, 24, 65, 29, 82, 48, 64,
## 71, 42, 37, 47, 93, 61, 68, 30, 60, 47, 84, 75, 58, 55, 41, 62,
## 53, 57, 42, 21, 60, 95, 88, 65, 65, 28, 67, 96, 29, 34, 56, 93,
## 70, 60, 47, 47, 36, 30, 96, 26, 48, 60, 80, 68, 30, 88, 47, 50,
## 33, 84, 66, 98, 44, 36, 50, 38, 48, 65, 70, 46, 39, 60, 74, 56,
## 16, 36, 52, 74, 89, 49, 38, 49, 72, 14, 54, 87, 82, 57, 36, 39,
## 55, 93, 99, 24, 52, 78, 27, 54, 51, 46, 60, 31, 46, 88, 44, 82,
## 73, 40, 65, 40, 75, 49, 100, 100, 52, 87, 66, 66, 63, 58, 64,
## 69, 47, 9, 47, 63, 35, 86, 44, 48, 33, 59, 52, 72, 41, 53, 57,
## 94, 30, 55, 55, 40, 75, 45, 65, 41, 56, 59, 35, 70, 47, 35, 33,
## 56, 84, 46, 33, 54, 64, 31, 55, 41, 33, 72, 41, 47, 39, 61, 57,
## 45, 54, 80, 55, 72, 21, 20, 86, 29, 46, 63, 63, 54, 29, 41, 31,
## 52, 34, 30, 52, 51, 51, 99, 43, 50, 32, 70, 40, 36, 18, 64, 39,
## 60, 52, 61, 69, 57, 57, 46, 35, 57, 34, 72, 24, 37, 66, 36, 13,
## 79, 37, 49, 33, 36, 90, 61, 61, 55, 48, 68, 62, 73, 86, 36, 99,
## 19, 33, 78, 64, 47, 72, 42, 48, 37, 29, 52, 98, 29, 89, 81, 87,
## 62, 54, 65, 59, 44, 57, 57, 73, 46, 70, 68, 48, 71, 34, 96, 42,
## 50, 48, 73, 43, 38, 89, 22, 63, 98, 55, 66, 45, 37, 29, 46, 66,
## 80, 82, 31, 52, 28, 54, 50, 31, 20, 55, 53, 79, 79, 51, 40, 45,
## 42, 33, 67, 35, 73, 35, 69, 76, 70, 73, 51, 83, 82, 36, 53, 53,
## 57, 35, 88, 37, 50, 40, 69, 32, 37, 33, 66, 77, 45, 83, 32, 45,
## 51, 56, 25, 80, 73, 60, 56, 17, 27, 34, 69, 93, 65, 69, 61, 94,
## 66, 34, 29, 40, 48, 53, 40, 51, 33, 59, 68, 41, 60, 80, 29, 85,
## 64, 57, 85, 21, 81, 94, 84, 49, 75, 34, 59, 84, 35, 100, 100,
## 60, 94, 57, 63, 74, 57, 60, 50, 39, 67, 85, 79, 26, 69, 88, 50,
## 45, 40, 53, 39, 37, 92, 45, 86, 55, 47, 62, 54, 54, 78, 54, 62,
## 74, 92, 44, 67, 54, 85, 51, 37, 96, 63, 61, 100, 58, 83, 40,
## 72, 75, 48, 43, 24, 66, 63, 71, 25, 50, 53, 43, 85, 46, 22, 66,
## 68, 53, 51, 95, 81, 57, 32, 53, 38, 80, 37, 46, 35, 77, 47, 81,
## 92, 68, 30, 53, 59, 43, 30, 76, 44, 88, 92, 49, 66, 64, 93, 60,
## 70, 93, 21, 30, 27, 44, 25, 86, 51, 25, 55, 31, 50, 53, 21, 24,
## 71, 20, 43, 72, 84, 55, 49, 77, 63, 70, 64, 36, 80, 39, 50, 45,
## 61, 41, 86, 26, 47, 61, 99, 63), P.Undergrad = c(537, 1227, 99,
## 63, 869, 230, 32, 78, 110, 44, 28, 1235, 287, 5, 281, 326, 1512,
## 23, 767, 7585, 726, 38, 300, 15, 538, 466, 1460, 266, 69, 3144,
## 484, 605, 131, 81, 501, 2, 1533, 62, 101, 82, 207, 27, 946, 129,
## 81, 3113, 8, 1213, 643, 62, 479, 822, 430, 1253, 16, 31, 148,
## 446, 868, 432, 1404, 1254, 136, 184, 434, 960, 331, 291, 737,
## 239, 580, 12, 764, 82, 526, 44, 40, 3881, 898, 33, 7, 209, 232,
## 3, 364, 1749, 13, 1, 296, 53, 422, 205, 222, 35, 25, 493, 1200,
## 1232, 103, 968, 894, 683, 173, 275, 22, 134, 1, 1829, 5346, 237,
## 55, 181, 172, 145, 232, 80, 644, 122, 336, 84, 536, 6, 283, 538,
## 14, 36, 62, 237, 45, 411, 56, 2458, 87, 48, 53, 1687, 2640, 1531,
## 845, 59, 23, 299, 436, 334, 32, 35, 16, 617, 82, 44, 233, 9310,
## 337, 436, 242, 68, 1197, 50, 63, 175, 691, 374, 258, 48, 406,
## 654, 9054, 785, 46, 963, 39, 166, 113, 2619, 314, 53, 35, 299,
## 24, 102, 1, 15, 334, 213, 67, 320, 5, 37, 6, 42, 275, 1350, 74,
## 399, 208, 126, 69, 519, 28, 1823, 23, 1305, 707, 1446, 1715,
## 166, 742, 71, 99, 392, 1569, 67, 43, 2246, 258, 1, 541, 44, 819,
## 1662, 226, 363, 20, 1957, 325, 341, 502, 132, 166, 336, 77, 59,
## 1423, 605, 33, 191, 840, 325, 118, 170, 158, 3757, 1822, 184,
## 761, 3417, 85, 280, 150, 113, 63, 246, 51, 254, 150, 1792, 653,
## 658, 377, 370, 776, 128, 1751, 402, 28, 684, 477, 80, 1260, 433,
## 1084, 911, 53, 807, 1532, 49, 179, 884, 721, 1621, 1014, 175,
## 11, 847, 416, 20, 1075, 153, 228, 12, 40, 435, 542, 88, 79, 466,
## 144, 352, 955, 505, 471, 1646, 411, 2814, 36, 334, 136, 871,
## 5481, 766, 1128, 266, 10221, 2682, 1979, 472, 60, 45, 382, 120,
## 35, 377, 66, 1310, 48, 705, 228, 1658, 936, 61, 942, 4379, 302,
## 139, 35, 529, 625, 1042, 83, 100, 30, 217, 1402, 214, 448, 30,
## 146, 1358, 72, 714, 472, 1938, 27, 56, 61, 16, 1309, 28, 1196,
## 239, 754, 118, 1489, 1052, 269, 3712, 1300, 1889, 94, 451, 222,
## 2196, 1140, 118, 105, 182, 216, 402, 5550, 128, 99, 7, 704, 1530,
## 300, 160, 602, 271, 95, 1103, 651, 2550, 387, 967, 3374, 546,
## 147, 43, 263, 107, 353, 131, 677, 45, 574, 248, 209, 418, 95,
## 34, 815, 388, 81, 11, 765, 926, 1231, 671, 1351, 1363, 2091,
## 346, 298, 1478, 475, 234, 1441, 166, 41, 38, 119, 81, 237, 2798,
## 660, 429, 3101, 351, 51, 902, 244, 639, 1534, 40, 144, 123, 4698,
## 2061, 864, 7152, 39, 2011, 1660, 73, 4522, 554, 2217, 131, 407,
## 3286, 2748, 1415, 2411, 911, 1673, 317, 503, 3991, 1940, 1630,
## 1339, 1254, 154, 21836, 804, 1583, 4552, 301, 331, 159, 1338,
## 1078, 1100, 1847, 1145, 1435, 3588, 5134, 1498, 30, 2582, 1605,
## 531, 174, 138, 2456, 594, 438, 549, 473, 1412, 3661, 10962, 1429,
## 2973, 1387, 3237, 8431, 5189, 5457, 39, 299, 433, 8374, 1674,
## 114, 4582, 2477, 579, 417, 1552, 2200, 7443, 1488, 1160, 17,
## 717, 198, 90, 1292, 338, 604, 67, 387, 20, 5, 117, 172, 497,
## 7, 105, 151, 3, 46, 1344, 1274, 474, 61, 110, 1550, 572, 27,
## 1904, 227, 170, 706, 98, 4278, 1116, 146, 506, 941, 37, 9, 56,
## 30, 305, 46, 30, 160, 2171, 603, 159, 120, 676, 872, 670, 22,
## 86, 2029, 1107, 166, 83, 1726), Books = c(450, 750, 400, 450,
## 800, 500, 450, 660, 500, 400, 400, 650, 450, 660, 550, 900, 500,
## 400, 350, 700, 540, 540, 600, 400, 750, 400, 1000, 500, 600,
## 600, 600, 750, 300, 355, 350, 600, 630, 550, 500, 650, 400, 500,
## 500, 450, 400, 475, 1495, 600, 2000, 410, 500, 500, 600, 860,
## 500, 800, 500, 300, 425, 612, 612, 600, 400, 600, 400, 500, 300,
## 450, 480, 400, 500, 600, 500, 570, 500, 600, 650, 500, 654, 600,
## 600, 600, 700, 400, 600, 525, 500, 500, 500, 700, 600, 500, 400,
## 500, 500, 550, 666, 400, 500, 380, 800, 600, 450, 450, 400, 600,
## 500, 470, 400, 500, 550, 450, 450, 400, 600, 500, 650, 400, 680,
## 450, 500, 600, 400, 500, 500, 550, 595, 600, 500, 400, 450, 450,
## 520, 500, 625, 500, 600, 650, 120, 600, 600, 500, 450, 490, 700,
## 475, 330, 350, 500, 500, 750, 800, 350, 400, 600, 525, 500, 600,
## 630, 600, 500, 500, 500, 550, 670, 795, 720, 500, 500, 531, 400,
## 600, 300, 500, 550, 400, 525, 450, 300, 450, 660, 500, 700, 700,
## 500, 500, 700, 500, 500, 400, 400, 1000, 500, 450, 465, 500,
## 600, 650, 600, 537, 400, 500, 700, 570, 640, 634, 500, 400, 400,
## 600, 500, 500, 450, 600, 500, 750, 400, 600, 600, 450, 600, 750,
## 920, 500, 600, 528, 400, 750, 400, 550, 600, 450, 500, 600, 350,
## 1000, 500, 225, 550, 500, 500, 600, 618, 600, 600, 700, 600,
## 450, 500, 500, 550, 450, 525, 500, 450, 450, 500, 550, 600, 575,
## 500, 500, 425, 600, 725, 500, 400, 600, 400, 425, 375, 540, 475,
## 500, 450, 550, 550, 1000, 600, 480, 600, 400, 400, 530, 550,
## 500, 600, 250, 500, 850, 750, 500, 500, 500, 550, 630, 400, 600,
## 700, 650, 550, 700, 600, 450, 500, 450, 500, 600, 600, 450, 600,
## 400, 600, 620, 470, 250, 450, 759, 500, 575, 558, 600, 600, 550,
## 550, 515, 500, 800, 420, 500, 616, 660, 600, 630, 450, 550, 500,
## 600, 600, 500, 650, 800, 400, 436, 598, 554, 675, 450, 450, 1000,
## 500, 600, 400, 370, 500, 1230, 700, 350, 600, 450, 500, 600,
## 500, 955, 550, 690, 690, 400, 450, 400, 600, 500, 800, 400, 550,
## 500, 500, 569, 612, 630, 500, 600, 600, 650, 450, 500, 550, 500,
## 500, 500, 450, 221, 576, 400, 500, 600, 550, 600, 600, 660, 385,
## 500, 400, 650, 300, 630, 675, 700, 425, 600, 500, 450, 600, 450,
## 711, 480, 700, 700, 600, 500, 550, 630, 620, 550, 600, 500, 1125,
## 400, 500, 400, 1000, 450, 400, 600, 650, 490, 600, 600, 500,
## 700, 500, 500, 350, 450, 600, 450, 750, 636, 790, 700, 500, 556,
## 700, 500, 530, 400, 600, 400, 700, 630, 525, 500, 687, 500, 700,
## 600, 400, 550, 500, 500, 476, 753, 600, 714, 600, 600, 500, 550,
## 300, 900, 650, 600, 550, 600, 500, 450, 600, 450, 540, 600, 765,
## 570, 500, 600, 630, 500, 700, 500, 750, 600, 500, 495, 500, 600,
## 500, 500, 750, 500, 650, 452, 1300, 646, 1200, 858, 500, 500,
## 708, 541, 376, 550, 300, 535, 570, 600, 500, 500, 450, 500, 630,
## 400, 500, 740, 500, 500, 500, 500, 585, 500, 500, 400, 400, 300,
## 680, 500, 800, 768, 540, 500, 650, 500, 850, 1400, 400, 600,
## 450, 110, 500, 500, 498, 500, 639, 500, 600, 490, 530, 700, 600,
## 750, 500, 678, 500, 550, 400, 550, 450, 300, 580, 500, 530, 500,
## 600, 617, 630, 500), PhD = c(70, 29, 53, 92, 76, 90, 89, 40,
## 82, 73, 79, 36, 78, 93, 48, 62, 60, 69, 55, 88, 65, 78, 66, 81,
## 59, 58, 68, 57, 83, 76, 71, 74, 78, 87, 64, 35, 87, 62, 61, 48,
## 74, 76, 66, 61, 76, 80, 93, 81, 75, 90, 71, 62, 39, 76, 100,
## 95, 77, 59, 87, 72, 72, 90, 75, 62, 90, 64, 10, 86, 74, 61, 74,
## 22, 58, 50, 41, 86, 76, 69, 67, 62, 95, 72, 71, 92, 81, 80, 69,
## 99, 94, 95, 67, 73, 64, 83, 95, 56, 73, 46, 70, 68, 66, 40, 53,
## 54, 92, 89, 84, 87, 87, 61, 97, 69, 67, 56, 86, 63, 85, 42, 68,
## 46, 61, 95, 58, 49, 88, 78, 87, 50, 52, 67, 61, 77, 93, 82, 95,
## 74, 73, 71, 62, 46, 82, 65, 71, 70, 79, 76, 62, 75, 53, 52, 90,
## 81, 45, 76, 57, 54, 50, 68, 59, 92, 47, 65, 67, 73, 91, 92, 87,
## 56, 94, 25, 73, 51, 53, 64, 64, 57, 65, 78, 91, 89, 95, 84, 75,
## 71, 75, 97, 100, 57, 82, 80, 75, 81, 78, 82, 72, 63, 31, 81,
## 75, 77, 77, 56, 49, 66, 81, 58, 77, 51, 68, 89, 96, 34, 97, 76,
## 63, 95, 66, 65, 57, 90, 93, 77, 91, 49, 61, 67, 84, 96, 88, 71,
## 58, 97, 36, 67, 71, 65, 89, 47, 74, 61, 64, 83, 66, 86, 77, 94,
## 73, 62, 48, 85, 49, 42, 63, 92, 97, 57, 37, 74, 66, 71, 77, 80,
## 52, 65, 99, 70, 57, 54, 93, 45, 73, 48, 68, 81, 72, 63, 82, 35,
## 77, 77, 49, 35, 91, 70, 71, 42, 76, 71, 48, 53, 79, 45, 44, 32,
## 77, 53, 85, 76, 72, 62, 77, 92, 99, 87, 57, 68, 65, 72, 92, 73,
## 79, 69, 73, 78, 73, 62, 59, 96, 71, 77, 91, 91, 73, 79, 93, 63,
## 58, 84, 62, 63, 56, 90, 78, 48, 76, 77, 95, 48, 58, 48, 100,
## 71, 45, 90, 55, 80, 91, 66, 69, 63, 73, 74, 77, 88, 90, 94, 84,
## 87, 59, 85, 60, 56, 44, 81, 79, 90, 90, 71, 70, 64, 55, 53, 84,
## 68, 82, 62, 68, 74, 87, 88, 51, 95, 83, 81, 80, 74, 66, 73, 85,
## 62, 55, 76, 74, 52, 70, 58, 56, 83, 50, 73, 48, 91, 86, 90, 43,
## 88, 84, 82, 74, 45, 69, 46, 85, 89, 78, 79, 93, 83, 91, 79, 71,
## 82, 82, 85, 80, 71, 80, 83, 91, 55, 56, 60, 59, 89, 81, 54, 65,
## 59, 81, 81, 91, 89, 98, 70, 70, 94, 96, 93, 96, 80, 99, 89, 89,
## 85, 82, 84, 72, 85, 60, 88, 88, 61, 85, 87, 88, 46, 67, 89, 88,
## 74, 90, 79, 74, 88, 81, 87, 71, 59, 72, 72, 89, 77, 88, 75, 82,
## 97, 82, 86, 75, 96, 86, 79, 95, 92, 79, 84, 75, 93, 86, 67, 62,
## 84, 84, 90, 56, 78, 86, 73, 91, 94, 16, 87, 94, 89, 87, 90, 96,
## 83, 78, 75, 90, 93, 79, 91, 69, 82, 39, 87, 93, 89, 61, 85, 51,
## 51, 43, 78, 67, 95, 42, 65, 66, 91, 81, 79, 84, 91, 60, 57, 53,
## 68, 10, 90, 76, 33, 58, 67, 84, 80, 74, 76, 83, 75, 66, 77, 81,
## 92, 66, 80, 84, 80, 88, 78, 91, 39, 67, 53, 71, 48, 92, 60, 73,
## 67, 96, 75), S.F.Ratio = c(18.1, 12.2, 12.9, 7.7, 11.9, 11.5,
## 13.7, 11.5, 11.3, 9.9, 15.3, 11.1, 14.7, 8.4, 12.1, 11.5, 23.1,
## 11.3, 12.7, 18.9, 12.8, 12.7, 10.4, 13, 22.4, 11, 17.6, 9.7,
## 10.3, 12.6, 18.5, 13.1, 13.2, 11.1, 14.1, 10.1, 17.5, 11.6, 8.8,
## 13.8, 14, 14.3, 18, 17.8, 13.3, 11.9, 11.2, 21.1, 14.4, 9.8,
## 13.7, 12.6, 13.1, 20.5, 12.3, 14.2, 10.9, 16.5, 13.9, 12.4, 19.8,
## 21.2, 14.8, 17.7, 14.6, 12.1, 12.1, 9.2, 17.8, 13.6, 15.9, 14.3,
## 11.7, 15.3, 9.5, 11.3, 13.5, 16.7, 18.1, 15.2, 11.4, 12.8, 8.3,
## 9.3, 11.1, 21.2, 16.9, 9.6, 10.5, 15.8, 18.1, 12.7, 12.1, 10.2,
## 10.5, 12.9, 17.2, 11.1, 13.1, 11.4, 14.3, 14, 9.5, 11.6, 11.3,
## 12.1, 11.1, 19.2, 15.3, 14.7, 5.9, 12.8, 12.1, 12.1, 10.7, 10.2,
## 6.5, 13, 14.6, 12.6, 22.2, 12, 12.8, 17.1, 11.6, 11.1, 11.2,
## 16.5, 14.1, 15.1, 12.5, 12.4, 10.2, 13.2, 5, 13.2, 14, 16.9,
## 16.2, 11.4, 12.8, 12.8, 11.3, 18.9, 13.9, 13.5, 10.6, 15.1, 12.5,
## 18.1, 10.6, 13.9, 21.5, 19.1, 14.9, 12.5, 17.6, 16.1, 10.5, 13.5,
## 13.3, 15.2, 20.1, 13.3, 7.2, 19.3, 19, 12.2, 12.1, 27.6, 14.2,
## 9.9, 15.3, 20.6, 13, 14.3, 18.4, 15.6, 9.6, 13, 13.3, 10.6, 13.7,
## 17.7, 12.3, 9.9, 8.2, 13, 13.1, 12, 10.6, 13.9, 11.1, 14.4, 12.5,
## 11.4, 12.9, 11.6, 15.6, 21, 12.9, 11.2, 39.8, 16, 19.2, 11.5,
## 17.9, 17, 13.3, 14.5, 3.3, 10.6, 12.7, 18.5, 12.4, 11.1, 15.6,
## 10.7, 14.2, 15.1, 10.5, 12.5, 10.7, 17.2, 16.1, 17, 12.3, 12.5,
## 12, 27.8, 20.8, 12.3, 14.3, 14.6, 12.6, 24.1, 17.8, 16.1, 18.4,
## 14.2, 10.5, 15.9, 20, 14.7, 11.7, 6.2, 13.8, 12.4, 12.6, 11.9,
## 10.8, 17.6, 11.8, 13.6, 11.3, 19, 8.4, 17.6, 6.8, 10.3, 10.6,
## 11.1, 13.1, 11.8, 10.1, 17.7, 11, 9.8, 9.2, 16.7, 16.8, 28.8,
## 14.1, 17.6, 16.8, 12, 12.7, 16.7, 16.5, 15.9, 15.8, 17.4, 11.6,
## 14.2, 16.4, 11.1, 18.1, 17.8, 13, 18.6, 9, 11.7, 11.3, 13.6,
## 12.8, 11.9, 16.7, 12.8, 20.2, 18.3, 13.6, 13.5, 13.7, 7.8, 11.4,
## 14.2, 14.2, 16.7, 17.5, 16.4, 17, 15.7, 12.9, 21.7, 17.3, 21.7,
## 14.8, 6.8, 13.1, 10.1, 10.5, 13.1, 14.5, 20.4, 12.1, 15.1, 16.2,
## 15.3, 13.9, 13.3, 14.9, 13.8, 11, 12.3, 10.9, 15, 11.6, 12.9,
## 11.6, 13.4, 10.4, 16.1, 14.5, 10.4, 19.4, 13.4, 8.4, 18.4, 16.3,
## 12, 19.6, 17.8, 10.7, 9.2, 11.8, 15.4, 12.3, 9.4, 12.2, 13, 10.7,
## 11.3, 16.4, 13.3, 12.9, 19.5, 18.6, 14.8, 14.5, 19.3, 14.8, 27.2,
## 4.6, 18.8, 10, 12.3, 11.2, 14.7, 19.5, 13.9, 11.8, 8.2, 16.8,
## 14.4, 18.8, 8.9, 15.8, 14.8, 10.3, 15, 19.6, 16.5, 13.5, 15.9,
## 19.9, 16.5, 11.8, 11.3, 10.6, 12.5, 15.4, 17.7, 14.5, 11.5, 14.5,
## 16.1, 11.6, 16.2, 15.1, 14, 16.1, 10.9, 12.5, 19, 19.5, 13, 17.4,
## 18, 10.5, 19, 18.7, 17.8, 16.3, 15.3, 17.9, 15.1, 14.9, 13.9,
## 6.5, 10, 15.5, 14.2, 8.9, 23.1, 14.8, 13.8, 18.2, 19, 12.1, 14.4,
## 10.4, 8.3, 9.1, 21.9, 12.2, 11.5, 6.7, 15.8, 16.1, 22.2, 5.3,
## 10.8, 16, 13.4, 18.3, 15.9, 13.5, 16.5, 15.8, 13.4, 14.7, 10.7,
## 11.8, 17.4, 13.7, 15.1, 15.2, 18.1, 16.7, 15, 11.5, 19, 14.6,
## 12.2, 20.3, 12.7, 13.4, 16.6, 18.9, 11.4, 17.5, 13, 8.9, 15.5,
## 19.1, 15.9, 17.8, 22.6, 21.5, 13.1, 11.5, 19.7, 6.3, 13.2, 15,
## 16.6, 11.7, 5.9, 13.6, 23.6, 14.8, 16.9, 17, 11.4, 22, 18.7,
## 16.5, 21, 19.7, 25.3, 7.5, 11.2, 11.5, 12.8, 9.9, 9.5, 9, 23.4,
## 21, 15.2, 23.1, 11.5, 15.9, 15.1, 17.4, 11.6, 10.5, 14.2, 5.8,
## 13.4, 16, 13.8, 13.7, 10.7, 22.9, 9.9, 13.2, 4.3, 11.3, 11.4,
## 12.4, 12.1, 9.6, 11.2, 16.9, 3.9, 20.3, 16.2, 15.1, 20.6, 15.4,
## 12.1, 15.3, 16.3, 16.4, 14.6, 12.5, 24.7, 15.4, 19.4, 22.7, 15.7,
## 12.5, 14.9, 12.7, 13.2, 14.1, 10.5, 13.6, 16.9, 12.6, 13.3, 13.3,
## 12.9, 8.3, 20.2, 12.8, 8.5, 15.2, 21, 13.3, 14.4, 5.8, 18.1),
## perc.alumni = c(12, 16, 30, 37, 2, 26, 37, 15, 31, 41, 32,
## 26, 19, 63, 14, 18, 5, 35, 25, 5, 31, 40, 30, 33, 11, 21,
## 20, 35, 33, 11, 38, 31, 10, 26, 18, 33, 20, 29, 32, 9, 34,
## 53, 19, 3, 19, 16, 52, 14, 21, 24, 12, 10, 26, 40, 49, 36,
## 29, 36, 25, 17, 13, 8, 41, 13, 26, 27, 24, 31, 25, 16, 22,
## 20, 39, 34, 20, 25, 29, 4, 0, 18, 60, 6, 29, 17, 24, 16,
## 31, 52, 35, 32, 9, 32, 39, 41, 45, 23, 18, 35, 26, 23, 28,
## 7, 19, 33, 55, 31, 43, 10, 2, 34, 21, 18, 9, 13, 40, 31,
## 32, 4, 42, 25, 10, 46, 19, 16, 45, 31, 39, 28, 12, 42, 17,
## 7, 28, 35, 44, 18, 9, 14, 5, 29, 26, 25, 21, 34, 51, 47,
## 31, 10, 9, 9, 7, 20, 24, 8, 8, 37, 16, 13, 14, 28, 18, 12,
## 26, 28, 27, 33, 10, 27, 32, 4, 32, 46, 26, 9, 31, 16, 18,
## 30, 60, 33, 53, 26, 10, 37, 32, 52, 46, 17, 26, 31, 34, 10,
## 48, 34, 40, 9, 4, 29, 30, 16, 34, 33, 15, 14, 22, 25, 29,
## 21, 19, 28, 38, 30, 37, 22, 14, 46, 37, 25, 14, 9, 38, 12,
## 19, 25, 10, 11, 30, 43, 20, 18, 23, 21, 10, 35, 8, 9, 34,
## 14, 23, 24, 11, 11, 13, 27, 14, 15, 38, 24, 15, 37, 33, 16,
## 20, 25, 24, 11, 21, 34, 50, 30, 17, 43, 13, 30, 35, 21, 11,
## 45, 15, 29, 22, 12, 30, 20, 20, 16, 38, 23, 18, 20, 8, 16,
## 43, 15, 31, 4, 19, 10, 32, 34, 51, 38, 30, 43, 36, 19, 35,
## 39, 27, 2, 24, 19, 11, 16, 32, 20, 17, 9, 21, 33, 24, 13,
## 17, 7, 11, 23, 20, 25, 22, 47, 30, 27, 31, 13, 32, 18, 8,
## 14, 30, 10, 25, 10, 23, 12, 22, 5, 13, 15, 19, 14, 11, 19,
## 10, 14, 1, 42, 54, 35, 32, 33, 9, 8, 38, 24, 37, 21, 23,
## 49, 19, 26, 21, 27, 8, 23, 30, 19, 12, 16, 29, 24, 19, 8,
## 19, 19, 31, 31, 46, 17, 7, 19, 23, 41, 20, 15, 13, 33, 36,
## 7, 44, 29, 9, 8, 17, 13, 11, 31, 12, 35, 40, 18, 9, 32, 29,
## 38, 8, 17, 23, 7, 36, 8, 13, 17, 24, 33, 7, 30, 16, 15, 7,
## 14, 12, 17, 10, 8, 16, 17, 8, 37, 48, 15, 7, 32, 16, 29,
## 23, 24, 21, 40, 41, 6, 48, 37, 21, 28, 7, 49, 16, 10, 11,
## 9, 36, 6, 16, 26, 15, 21, 14, 18, 26, 20, 22, 9, 6, 13, 17,
## 4, 11, 12, 15, 20, 26, 11, 16, 37, 14, 15, 15, 4, 8, 13,
## 16, 11, 23, 17, 15, 16, 14, 6, 8, 46, 11, 13, 38, 17, 17,
## 7, 32, 23, 8, 3, 3, 18, 7, 10, 21, 23, 22, 4, 11, 3, 9, 14,
## 10, 9, 10, 22, 10, 12, 17, 15, 16, 20, 8, 13, 19, 40, 15,
## 23, 26, 24, 11, 20, 8, 31, 3, 55, 23, 37, 33, 20, 37, 40,
## 45, 37, 30, 31, 29, 26, 4, 14, 8, 39, 16, 10, 42, 9, 39,
## 11, 15, 4, 10, 20, 20, 17, 40, 41, 27, 51, 29, 20, 19, 24,
## 37, 16, 43, 18, 26, 26, 34, 14, 31, 20, 49, 28), Expend = c(7041,
## 10527, 8735, 19016, 10922, 8861, 11487, 8991, 10932, 11711,
## 9305, 8127, 7355, 21424, 7994, 10908, 4010, 42926, 6584,
## 4602, 7836, 9220, 6871, 11361, 6523, 6136, 8086, 9337, 12580,
## 9084, 7503, 6668, 7550, 12957, 5922, 16364, 10941, 7718,
## 8324, 6817, 8649, 8377, 7041, 6259, 9073, 16836, 20447, 6918,
## 7671, 17150, 5935, 4900, 8355, 7916, 17449, 13675, 9511,
## 7117, 7922, 8985, 8453, 7268, 7786, 5391, 7972, 9557, 7976,
## 24386, 7666, 6716, 7364, 7697, 10961, 6897, 9583, 9685, 8444,
## 4900, 6413, 3365, 13118, 12692, 7729, 10922, 8129, 4639,
## 7083, 18443, 11951, 11659, 4417, 10141, 8741, 15954, 15494,
## 8604, 4776, 6889, 8847, 9447, 6084, 8820, 6936, 8996, 12138,
## 9534, 14140, 7850, 5015, 8693, 30639, 6955, 6875, 7309, 14773,
## 10965, 22906, 8189, 6898, 8686, 8643, 17581, 7505, 5113,
## 12423, 11525, 13861, 4525, 7566, 6852, 7325, 11178, 14907,
## 9303, 27206, 9002, 9825, 5719, 5682, 10188, 15003, 9815,
## 8952, 6329, 8061, 7527, 9552, 6972, 7967, 3930, 8923, 6722,
## 4607, 5039, 6336, 11751, 6418, 6078, 8095, 12940, 7711, 5664,
## 6786, 7508, 19635, 11271, 7762, 7348, 14720, 6081, 9226,
## 10270, 9798, 5063, 7949, 8222, 4957, 9114, 17761, 10296,
## 12263, 9248, 7054, 6466, 11625, 37219, 21569, 7335, 8588,
## 12639, 12165, 10093, 13957, 12434, 9284, 7703, 9249, 8324,
## 7348, 5569, 9605, 7305, 6562, 8107, 8420, 9812, 5212, 3186,
## 8118, 7738, 56233, 7840, 12067, 6122, 6535, 14067, 7649,
## 8954, 7022, 9084, 15365, 9067, 15687, 4054, 5531, 6119, 8196,
## 14665, 8539, 8694, 6863, 12999, 7701, 5177, 10912, 3480,
## 8747, 6374, 5553, 7578, 7547, 6741, 4546, 9448, 9456, 13009,
## 8949, 8832, 7114, 14213, 10642, 4796, 7940, 10062, 11291,
## 5801, 5352, 8408, 10819, 10502, 8575, 8317, 5925, 9034, 33541,
## 6652, 6383, 9754, 8995, 7307, 8707, 3871, 7762, 7846, 7832,
## 8128, 11218, 7140, 6170, 6223, 5704, 4333, 11087, 9492, 6112,
## 11989, 4795, 8122, 8111, 6990, 18359, 5073, 6695, 6525, 8536,
## 10613, 7215, 10888, 5972, 7905, 8797, 12529, 9241, 21227,
## 5788, 7788, 6562, 7090, 9670, 8871, 6310, 6601, 9563, 6157,
## 6086, 5284, 6261, 26385, 9209, 16593, 16196, 8568, 9979,
## 8811, 12011, 5511, 6578, 6433, 8802, 6413, 7114, 10059, 9431,
## 9157, 11216, 6443, 16185, 8028, 8990, 5557, 14820, 7895,
## 7652, 14329, 5967, 8354, 28320, 8135, 6880, 8847, 4519, 7333,
## 11080, 16358, 15886, 15605, 11299, 12472, 6744, 9405, 7519,
## 6422, 7957, 11561, 9264, 10474, 10134, 7120, 6719, 7344,
## 7360, 4322, 18367, 5081, 12502, 8534, 9599, 9533, 7930, 10872,
## 8545, 18372, 10368, 10080, 6719, 14086, 7411, 7881, 21199,
## 5084, 4444, 7498, 12726, 4718, 4632, 6591, 7818, 12995, 6860,
## 9988, 10938, 9828, 7908, 14980, 9209, 9619, 10357, 7651,
## 8595, 8426, 6534, 9995, 10307, 12837, 5599, 7495, 9075, 8055,
## 13705, 6632, 7511, 5563, 6442, 6608, 6174, 6436, 8170, 10554,
## 18953, 7233, 5970, 8294, 6286, 8471, 9158, 7002, 3605, 5096,
## 10219, 8504, 18034, 11806, 16920, 4933, 10872, 15411, 16352,
## 13919, 15934, 6742, 36854, 13889, 10178, 8731, 10650, 11762,
## 10891, 8767, 7780, 14737, 7881, 10625, 12833, 8559, 9657,
## 5935, 6408, 9021, 10276, 7462, 14847, 6393, 6716, 16122,
## 6971, 10145, 6433, 5412, 5883, 9718, 7855, 7011, 15893, 7392,
## 6005, 9424, 6104, 5657, 6309, 13936, 10244, 8020, 25765,
## 9060, 11217, 9158, 11984, 26037, 10074, 3864, 5035, 8246,
## 11020, 17007, 4078, 5917, 8612, 4696, 7837, 4329, 11641,
## 13706, 11743, 9275, 12646, 13597, 16527, 8488, 6254, 6490,
## 5559, 11006, 8094, 8745, 3733, 12082, 7164, 9681, 23850,
## 10458, 5733, 8944, 6757, 8050, 5861, 14904, 9006, 41766,
## 5738, 9430, 7735, 10162, 15736, 10830, 10912, 45702, 4550,
## 6563, 4839, 6951, 17858, 16262, 6773, 4249, 8080, 6554, 10026,
## 5983, 8409, 4599, 7203, 4222, 7925, 8837, 11916, 22704, 7494,
## 13198, 11778, 8328, 9603, 8543, 10779, 7438, 10291, 5318,
## 6729, 8960, 10774, 4469, 9189, 8323, 40386, 4509), Grad.Rate = c(60,
## 56, 54, 59, 15, 63, 73, 52, 73, 76, 68, 55, 69, 100, 59,
## 46, 34, 48, 65, 48, 58, 71, 69, 71, 48, 65, 85, 71, 91, 72,
## 72, 84, 52, 69, 58, 55, 82, 48, 56, 58, 72, 51, 75, 53, 58,
## 72, 96, 67, 85, 84, 49, 18, 58, 33, 89, 93, 83, 71, 55, 60,
## 59, 61, 81, 49, 64, 83, 52, 74, 79, 67, 62, 118, 74, 64,
## 24, 66, 67, 49, 51, 58, 74, 47, 73, 58, 63, 48, 21, 87, 79,
## 77, 46, 67, 75, 91, 93, 96, 51, 100, 72, 78, 64, 80, 76,
## 72, 95, 93, 69, 59, 37, 76, 99, 45, 42, 75, 91, 75, 85, 63,
## 46, 54, 72, 94, 56, 58, 81, 82, 87, 46, 61, 60, 87, 42, 83,
## 67, 97, 58, 42, 50, 76, 82, 59, 81, 86, 63, 82, 67, 53, 24,
## 22, 69, 57, 66, 62, 43, 83, 60, 51, 62, 54, 82, 65, 29, 74,
## 55, 95, 70, 34, 76, 83, 36, 66, 72, 64, 57, 39, 60, 100,
## 65, 91, 65, 69, 64, 38, 73, 73, 100, 100, 52, 63, 79, 79,
## 60, 72, 72, 72, 44, 21, 75, 52, 54, 83, 69, 34, 66, 65, 75,
## 98, 54, 75, 89, 90, 56, 80, 54, 68, 88, 87, 65, 52, 84, 92,
## 75, 77, 57, 60, 51, 85, 91, 66, 58, 56, 69, 61, 53, 45, 100,
## 81, 63, 62, 70, 59, 37, 45, 80, 53, 65, 77, 70, 51, 77, 59,
## 55, 64, 79, 70, 68, 59, 69, 90, 77, 55, 51, 61, 66, 94, 52,
## 32, 48, 91, 78, 80, 59, 89, 85, 71, 64, 58, 67, 61, 53, 63,
## 27, 56, 54, 74, 15, 60, 83, 56, 60, 84, 44, 64, 21, 80, 72,
## 81, 83, 52, 71, 61, 72, 34, 71, 83, 65, 57, 44, 62, 76, 42,
## 76, 46, 41, 56, 54, 58, 92, 63, 83, 79, 67, 83, 64, 75, 50,
## 45, 48, 87, 65, 37, 62, 83, 69, 42, 48, 66, 68, 39, 61, 73,
## 54, 66, 62, 35, 85, 99, 96, 80, 86, 62, 47, 74, 68, 68, 70,
## 70, 64, 81, 72, 79, 68, 61, 90, 81, 77, 57, 82, 97, 69, 67,
## 85, 67, 78, 83, 88, 60, 61, 41, 100, 52, 73, 66, 64, 72,
## 79, 70, 48, 90, 67, 53, 43, 72, 71, 56, 51, 52, 67, 89, 65,
## 49, 78, 66, 85, 40, 78, 63, 72, 88, 45, 67, 59, 73, 79, 64,
## 97, 74, 80, 57, 49, 42, 53, 66, 53, 65, 59, 46, 90, 61, 53,
## 46, 98, 36, 69, 64, 50, 10, 39, 70, 81, 91, 96, 74, 52, 65,
## 88, 33, 78, 66, 46, 90, 54, 71, 63, 75, 67, 51, 45, 77, 66,
## 63, 66, 54, 81, 57, 64, 35, 63, 68, 56, 87, 53, 51, 45, 53,
## 58, 48, 52, 51, 64, 75, 37, 83, 53, 55, 49, 47, 35, 40, 97,
## 44, 54, 93, 72, 63, 63, 100, 80, 62, 43, 48, 63, 47, 68,
## 38, 45, 53, 29, 65, 50, 57, 65, 47, 37, 79, 95, 65, 53, 65,
## 36, 67, 72, 38, 45, 78, 79, 68, 95, 83, 96, 31, 73, 30, 73,
## 58, 72, 75, 89, 68, 63, 67, 86, 90, 65, 56, 90, 52, 63, 90,
## 48, 64, 92, 52, 60, 67, 55, 60, 55, 59, 52, 61, 65, 62, 87,
## 85, 71, 72, 72, 52, 80, 63, 67, 68, 52, 67, 58, 59, 50, 82,
## 40, 83, 49, 99, 99), .outcome = c(7440, 12280, 11250, 12960,
## 7560, 13290, 13868, 10468, 16548, 17080, 12572, 8352, 8700,
## 19760, 10100, 9996, 5130, 15476, 11208, 7434, 11902, 13353,
## 10990, 11280, 9925, 8620, 10995, 9690, 17926, 11290, 6450,
## 8840, 9000, 16304, 9550, 21700, 13800, 8740, 8540, 5188,
## 11660, 6500, 7844, 7150, 9900, 18420, 19030, 7452, 10870,
## 19380, 9592, 4371, 10260, 2340, 18165, 18550, 13130, 10518,
## 8900, 12950, 7380, 7706, 10230, 6060, 10750, 13050, 8400,
## 17900, 12200, 8150, 13125, 9384, 14340, 7344, 11400, 8950,
## 10938, 5962, 7242, 8300, 11850, 16624, 10335, 8730, 9300,
## 7860, 4412, 17000, 17500, 15960, 7168, 13925, 9888, 18930,
## 19510, 10860, 6120, 9800, 12247, 10900, 9990, 11138, 8300,
## 11844, 18000, 11720, 16240, 8412, 8294, 10425, 18624, 10500,
## 6900, 9216, 18740, 12050, 10628, 6230, 8920, 9130, 12292,
## 17295, 10850, 4528, 16900, 14300, 18700, 4486, 6700, 9570,
## 9800, 9000, 18432, 8730, 18590, 7248, 5800, 5962, 5710, 9650,
## 15360, 14190, 11800, 9100, 8578, 10485, 10955, 6806, 9400,
## 5120, 13900, 6597, 8390, 5840, 9650, 10390, 13320, 5500,
## 9900, 13440, 10970, 8180, 9476, 8100, 18300, 6489, 6744,
## 9150, 19964, 6120, 12200, 9420, 8958, 6108, 8330, 10310,
## 5224, 13404, 19700, 13252, 13218, 8200, 6300, 5504, 17480,
## 18485, 17230, 9376, 8800, 11090, 14067, 11600, 13470, 13960,
## 12275, 8080, 7260, 10500, 8050, 7799, 14360, 10000, 9210,
## 10690, 7550, 14424, 7994, 7620, 6398, 11700, 18800, 9414,
## 14850, 6995, 8400, 19240, 10910, 8664, 8842, 12600, 18730,
## 6987, 16880, 9400, 5170, 4938, 13850, 18700, 10100, 11700,
## 8840, 15800, 10560, 5950, 4818, 9200, 13380, 7352, 7920,
## 11200, 5150, 5925, 3957, 12990, 11100, 11500, 13240, 12450,
## 7320, 15909, 9620, 9858, 10440, 12370, 14700, 4300, 9400,
## 10700, 11200, 11510, 11390, 11200, 9250, 11040, 20100, 7680,
## 6930, 7950, 11985, 9813, 12500, 5016, 10300, 8856, 7844,
## 8200, 11320, 11505, 5580, 9866, 4386, 8550, 13000, 12480,
## 6073, 8438, 4426, 7050, 10520, 4515, 19300, 6844, 10500,
## 9900, 12850, 12474, 12250, 16975, 4738, 9090, 10850, 8832,
## 5376, 17748, 10194, 10320, 5542, 6806, 8400, 11718, 5834,
## 4856, 13380, 6746, 7799, 3735, 9840, 16404, 14134, 19670,
## 16560, 12900, 15990, 7629, 16732, 5390, 6400, 5336, 12888,
## 6530, 8530, 11000, 13312, 11925, 14210, 6360, 18200, 11690,
## 10500, 6000, 17688, 10178, 9700, 16200, 4290, 11859, 19900,
## 14400, 10100, 12030, 6684, 4449, 13840, 13970, 19960, 17475,
## 13250, 15200, 9870, 13425, 9490, 8734, 12520, 16425, 10950,
## 7410, 7411, 11070, 12950, 10880, 11200, 9985, 11690, 10800,
## 14350, 10850, 10475, 8236, 8384, 13584, 8955, 17238, 12669,
## 12000, 7844, 16160, 11250, 8990, 18820, 3811, 3738, 5472,
## 12772, 7070, 4740, 4285, 7200, 11850, 8400, 7000, 8600, 10456,
## 10570, 18720, 11550, 13332, 6800, 8678, 12140, 5000, 8650,
## 13900, 12315, 16900, 3040, 12170, 6550, 6550, 6550, 6550,
## 6550, 6550, 6550, 6550, 6550, 6840, 6550, 16130, 14500, 7850,
## 5666, 10965, 7070, 5130, 8490, 7850, 7860, 7600, 10900, 5391,
## 18810, 11412, 19040, 7700, 6735, 18732, 4440, 11648, 12024,
## 6618, 18930, 8907, 11656, 10760, 10220, 15192, 11130, 10430,
## 11800, 7090, 5697, 14220, 4460, 7560, 6994, 6600, 6600, 8723,
## 8566, 6919, 15732, 8828, 9843, 8949, 4916, 9057, 7246, 6150,
## 4440, 11450, 11180, 5972, 8400, 8677, 7558, 5634, 6634, 4104,
## 7731, 16850, 5173, 10602, 17020, 12040, 16230, 10330, 14500,
## 17840, 13226, 3687, 5800, 8074, 6760, 17230, 4973, 4652,
## 5764, 4422, 5130, 4104, 12520, 16320, 11750, 6857, 15516,
## 12212, 8199, 6172, 6704, 7032, 6950, 9096, 8786, 5988, 8840,
## 14900, 9600, 11800, 17865, 15925, 5587, 10260, 7384, 9140,
## 4450, 12925, 13500, 13850, 8670, 10000, 11600, 16260, 13750,
## 15276, 8200, 18350, 2700, 8840, 5590, 9160, 9850, 19130,
## 7844, 4470, 14200, 6390, 14510, 6940, 8994, 5918, 8124, 5542,
## 10720, 14320, 11480, 18460, 10500, 16670, 16249, 12660, 12350,
## 11150, 14800, 10535, 11428, 4200, 6400, 9100, 15884, 6797,
## 11520, 6900, 19840, 4990)), row.names = c("Abilene.Christian.University",
## "Adelphi.University", "Adrian.College", "Agnes.Scott.College",
## "Alaska.Pacific.University", "Albertus.Magnus.College", "Albion.College",
## "Alderson.Broaddus.College", "Alfred.University", "Allegheny.College",
## "Alma.College", "Alverno.College", "American.International.College",
## "Amherst.College", "Anderson.University", "Andrews.University",
## "Angelo.State.University", "Antioch.University", "Aquinas.College",
## "Arizona.State.University.Main.campus", "Augsburg.College", "Augustana.College.IL",
## "Augustana.College", "Austin.College", "Averett.College", "Baker.University",
## "Baldwin.Wallace.College", "Barat.College", "Barnard.College",
## "Barry.University", "Baylor.University", "Bellarmine.College",
## "Belmont.Abbey.College", "Beloit.College", "Benedictine.College",
## "Bennington.College", "Bentley.College", "Bethany.College", "Bethel.College.KS",
## "Bethune.Cookman.College", "Birmingham.Southern.College", "Blackburn.College",
## "Bloomsburg.Univ..of.Pennsylvania", "Bluefield.College", "Bluffton.College",
## "Boston.University", "Bowdoin.College", "Bowling.Green.State.University",
## "Bradley.University", "Brandeis.University", "Brenau.University",
## "Brewton.Parker.College", "Briar.Cliff.College", "Brigham.Young.University.at.Provo",
## "Bryn.Mawr.College", "Bucknell.University", "Butler.University",
## "Cabrini.College", "Caldwell.College", "California.Lutheran.University",
## "California.Polytechnic.San.Luis", "California.State.University.at.Fresno",
## "Calvin.College", "Campbellsville.College", "Canisius.College",
## "Capital.University", "Capitol.College", "Carnegie.Mellon.University",
## "Carroll.College", "Carson.Newman.College", "Carthage.College",
## "Cazenovia.College", "Cedar.Crest.College", "Cedarville.College",
## "Centenary.College", "Centenary.College.of.Louisiana", "Central.College",
## "Central.Connecticut.State.University", "Central.Washington.University",
## "Central.Wesleyan.College", "Centre.College", "Chapman.University",
## "Chestnut.Hill.College", "Christendom.College", "Christian.Brothers.University",
## "Christopher.Newport.University", "Claflin.College", "Claremont.McKenna.College",
## "Clark.University", "Clarkson.University", "Clinch.Valley.Coll..of..the.Univ..of.Virginia",
## "Coe.College", "Coker.College", "Colby.College", "Colgate.University",
## "College.Misericordia", "College.of.Charleston", "College.of.Mount.St..Joseph",
## "College.of.Saint.Benedict", "College.of.Saint.Elizabeth", "College.of.Saint.Rose",
## "College.of.Santa.Fe", "College.of.St..Joseph", "College.of.St..Scholastica",
## "College.of.the.Holy.Cross", "College.of.William.and.Mary", "College.of.Wooster",
## "Colorado.State.University", "Columbia.College.MO", "Columbia.College",
## "Columbia.University", "Concordia.College.at.St..Paul", "Concordia.Lutheran.College",
## "Concordia.University", "Connecticut.College", "Converse.College",
## "Creighton.University", "Cumberland.College", "D.Youville.College",
## "Dana.College", "Daniel.Webster.College", "Davidson.College",
## "Defiance.College", "Delta.State.University", "Denison.University",
## "DePauw.University", "Dickinson.College", "Dickinson.State.University",
## "Dillard.University", "Doane.College", "Dordt.College", "Dowling.College",
## "Drew.University", "Drury.College", "Duke.University", "East.Carolina.University",
## "East.Tennessee.State.University", "Eastern.Connecticut.State.University",
## "Eastern.Illinois.University", "Eastern.Mennonite.College", "Eckerd.College",
## "Elizabethtown.College", "Elms.College", "Elon.College", "Emory...Henry.College",
## "Erskine.College", "Eureka.College", "Fayetteville.State.University",
## "Ferrum.College", "Flagler.College", "Florida.Institute.of.Technology",
## "Florida.International.University", "Fontbonne.College", "Francis.Marion.University",
## "Franciscan.University.of.Steubenville", "Franklin.College",
## "Franklin.Pierce.College", "Freed.Hardeman.University", "Fresno.Pacific.College",
## "Furman.University", "Gannon.University", "Gardner.Webb.University",
## "Geneva.College", "Georgetown.College", "Georgetown.University",
## "Georgia.Institute.of.Technology", "Georgia.State.University",
## "Georgian.Court.College", "Gettysburg.College", "Goldey.Beacom.College",
## "Gordon.College", "Goshen.College", "Grace.College.and.Seminary",
## "Grand.Valley.State.University", "Greensboro.College", "Greenville.College",
## "Grove.City.College", "Guilford.College", "Hamilton.College",
## "Hamline.University", "Hampden...Sydney.College", "Hanover.College",
## "Hardin.Simmons.University", "Harding.University", "Hartwick.College",
## "Harvard.University", "Harvey.Mudd.College", "Hastings.College",
## "Hendrix.College", "Hillsdale.College", "Hiram.College", "Hofstra.University",
## "Hollins.College", "Hood.College", "Hope.College", "Huntingdon.College",
## "Huron.University", "Illinois.Benedictine.College", "Illinois.College",
## "Illinois.State.University", "Illinois.Wesleyan.University",
## "Immaculata.College", "Indiana.Wesleyan.University", "Iona.College",
## "Iowa.State.University", "Ithaca.College", "James.Madison.University",
## "Jamestown.College", "John.Brown.University", "John.Carroll.University",
## "Johns.Hopkins.University", "Judson.College", "Juniata.College",
## "Kansas.State.University", "Kansas.Wesleyan.University", "Kenyon.College",
## "King.s.College", "King.College", "La.Roche.College", "La.Salle.University",
## "Lafayette.College", "LaGrange.College", "Lake.Forest.College",
## "Lakeland.College", "Lambuth.University", "Lander.University",
## "Lebanon.Valley.College", "Lehigh.University", "Lenoir.Rhyne.College",
## "Lesley.College", "LeTourneau.University", "Lewis.and.Clark.College",
## "Lewis.University", "Lincoln.Memorial.University", "Lincoln.University",
## "Lindenwood.College", "Linfield.College", "Lock.Haven.University.of.Pennsylvania",
## "Longwood.College", "Loras.College", "Louisiana.College", "Louisiana.State.University.at.Baton.Rouge",
## "Louisiana.Tech.University", "Loyola.College", "Loyola.University",
## "Loyola.University.Chicago", "Luther.College", "Lynchburg.College",
## "Lyndon.State.College", "Macalester.College", "MacMurray.College",
## "Malone.College", "Manchester.College", "Manhattan.College",
## "Manhattanville.College", "Mankato.State.University", "Marian.College.of.Fond.du.Lac",
## "Marist.College", "Mary.Baldwin.College", "Marymount.College.Tarrytown",
## "Marymount.University", "Maryville.College", "Maryville.University",
## "Marywood.College", "Massachusetts.Institute.of.Technology",
## "McKendree.College", "McMurry.University", "McPherson.College",
## "Mercer.University", "Mercyhurst.College", "Merrimack.College",
## "Mesa.State.College", "Messiah.College", "Miami.University.at.Oxford",
## "Millersville.University.of.Penn.", "Milligan.College", "Millsaps.College",
## "Milwaukee.School.of.Engineering", "Mississippi.College", "Mississippi.State.University",
## "Mississippi.University.for.Women", "Missouri.Valley.College",
## "Monmouth.College.IL", "Monmouth.College", "Montana.College.of.Mineral.Sci....Tech.",
## "Montreat.Anderson.College", "Moorhead.State.University", "Morehouse.College",
## "Morningside.College", "Morris.College", "Mount.Holyoke.College",
## "Mount.Marty.College", "Mount.Mercy.College", "Mount.Saint.Clare.College",
## "Mount.Saint.Mary.s.College", "Mount.St..Mary.s.College", "Mount.Union.College",
## "Muhlenberg.College", "Murray.State.University", "National.Louis.University",
## "Nazareth.College.of.Rochester", "New.Jersey.Institute.of.Technology",
## "New.Mexico.Institute.of.Mining.and.Tech.", "New.York.University",
## "Newberry.College", "Niagara.University", "North.Adams.State.College",
## "North.Carolina.A....T..State.University", "North.Carolina.State.University.at.Raleigh",
## "North.Central.College", "North.Dakota.State.University", "Northeast.Missouri.State.University",
## "Northeastern.University", "Northern.Arizona.University", "Northern.Illinois.University",
## "Northwest.Missouri.State.University", "Northwest.Nazarene.College",
## "Northwestern.University", "Norwich.University", "Oberlin.College",
## "Occidental.College", "Oglethorpe.University", "Ohio.Northern.University",
## "Ohio.University", "Ohio.Wesleyan.University", "Oklahoma.Baptist.University",
## "Oklahoma.Christian.University", "Oklahoma.State.University",
## "Otterbein.College", "Ouachita.Baptist.University", "Our.Lady.of.the.Lake.University",
## "Pace.University", "Pacific.Lutheran.University", "Pacific.Union.College",
## "Pacific.University", "Pembroke.State.University", "Pepperdine.University",
## "Philadelphia.Coll..of.Textiles.and.Sci.", "Phillips.University",
## "Pikeville.College", "Pitzer.College", "Point.Loma.Nazarene.College",
## "Point.Park.College", "Polytechnic.University", "Prairie.View.A..and.M..University",
## "Presbyterian.College", "Princeton.University", "Providence.College",
## "Quincy.University", "Quinnipiac.College", "Radford.University",
## "Ramapo.College.of.New.Jersey", "Randolph.Macon.College", "Randolph.Macon.Woman.s.College",
## "Reed.College", "Rensselaer.Polytechnic.Institute", "Rider.University",
## "Ripon.College", "Rivier.College", "Roanoke.College", "Rockhurst.College",
## "Rocky.Mountain.College", "Roger.Williams.University", "Rollins.College",
## "Rosary.College", "Rutgers.at.New.Brunswick", "Rutgers.State.University.at.Camden",
## "Sacred.Heart.University", "Saint.Anselm.College", "Saint.Francis.College",
## "Saint.Joseph.s.College.IN", "Saint.Joseph.s.College", "Saint.Louis.University",
## "Saint.Mary.s.College.of.Minnesota", "Saint.Olaf.College", "Saint.Vincent.College",
## "Salem.College", "Samford.University", "San.Diego.State.University",
## "Santa.Clara.University", "Schreiner.College", "Scripps.College",
## "Seattle.Pacific.University", "Seton.Hall.University", "Shippensburg.University.of.Penn.",
## "Simmons.College", "Simpson.College", "Sioux.Falls.College",
## "Smith.College", "South.Dakota.State.University", "Southeastern.Oklahoma.State.Univ.",
## "Southern.Illinois.University.at.Edwardsville", "Southern.Methodist.University",
## "Southwest.Baptist.University", "Southwest.Missouri.State.University",
## "Southwest.State.University", "Southwestern.College", "Southwestern.University",
## "Spalding.University", "Spelman.College", "Spring.Arbor.College",
## "St..Bonaventure.University", "St..John.Fisher.College", "St..Lawrence.University",
## "St..Martin.s.College", "St..Mary.s.College.of.California", "St..Mary.s.College.of.Maryland",
## "St..Mary.s.University.of.San.Antonio", "St..Norbert.College",
## "St..Paul.s.College", "St..Thomas.Aquinas.College", "Stephens.College",
## "Stetson.University", "Stevens.Institute.of.Technology", "Stockton.College.of.New.Jersey",
## "Stonehill.College", "SUNY.at.Albany", "SUNY.at.Binghamton",
## "SUNY.at.Stony.Brook", "SUNY.College..at.Brockport", "SUNY.College.at.Buffalo",
## "SUNY.College.at.Cortland", "SUNY.College.at.Fredonia", "SUNY.College.at.New.Paltz",
## "SUNY.College.at.Plattsburgh", "SUNY.College.at.Potsdam", "SUNY.College.at.Purchase",
## "Susquehanna.University", "Sweet.Briar.College", "Tabor.College",
## "Talladega.College", "Taylor.University", "Tennessee.Wesleyan.College",
## "Texas.A.M.Univ..at.College.Station", "Texas.Christian.University",
## "Texas.Lutheran.College", "Texas.Southern.University", "Tiffin.University",
## "Transylvania.University", "Trenton.State.College", "Trinity.College.CT",
## "Trinity.College.DC", "Tulane.University", "Tusculum.College",
## "Tuskegee.University", "Union.College.NY", "University.of.Alabama.at.Birmingham",
## "University.of.California.at.Berkeley", "University.of.California.at.Irvine",
## "University.of.Central.Florida", "University.of.Chicago", "University.of.Cincinnati",
## "University.of.Connecticut.at.Storrs", "University.of.Dallas",
## "University.of.Delaware", "University.of.Denver", "University.of.Detroit.Mercy",
## "University.of.Dubuque", "University.of.Evansville", "University.of.Florida",
## "University.of.Georgia", "University.of.Hartford", "University.of.Hawaii.at.Manoa",
## "University.of.Illinois...Urbana", "University.of.Kansas", "University.of.Maine.at.Machias",
## "University.of.Maine.at.Presque.Isle", "University.of.Maryland.at.College.Park",
## "University.of.Massachusetts.at.Amherst", "University.of.Massachusetts.at.Dartmouth",
## "University.of.Michigan.at.Ann.Arbor", "University.of.Minnesota.at.Duluth",
## "University.of.Minnesota.at.Morris", "University.of.Minnesota.Twin.Cities",
## "University.of.Mississippi", "University.of.Missouri.at.Columbia",
## "University.of.Missouri.at.Saint.Louis", "University.of.Mobile",
## "University.of.Montevallo", "University.of.New.England", "University.of.New.Hampshire",
## "University.of.North.Carolina.at.Asheville", "University.of.North.Carolina.at.Chapel.Hill",
## "University.of.North.Carolina.at.Greensboro", "University.of.North.Carolina.at.Wilmington",
## "University.of.North.Dakota", "University.of.North.Florida",
## "University.of.North.Texas", "University.of.Northern.Colorado",
## "University.of.Notre.Dame", "University.of.Oklahoma", "University.of.Oregon",
## "University.of.Pennsylvania", "University.of.Portland", "University.of.Puget.Sound",
## "University.of.Rhode.Island", "University.of.Richmond", "University.of.Rochester",
## "University.of.San.Francisco", "University.of.Sci..and.Arts.of.Oklahoma",
## "University.of.South.Carolina.at.Aiken", "University.of.South.Carolina.at.Columbia",
## "University.of.South.Florida", "University.of.Southern.California",
## "University.of.Southern.Indiana", "University.of.Southern.Mississippi",
## "University.of.Tennessee.at.Knoxville", "University.of.Texas.at.Arlington",
## "University.of.Texas.at.Austin", "University.of.Texas.at.San.Antonio",
## "University.of.the.Arts", "University.of.the.Pacific", "University.of.Tulsa",
## "University.of.Utah", "University.of.Vermont", "University.of.Virginia",
## "University.of.Washington", "University.of.West.Florida", "University.of.Wisconsin.Stout",
## "University.of.Wisconsin.Superior", "University.of.Wisconsin.Whitewater",
## "University.of.Wisconsin.at.Madison", "University.of.Wisconsin.at.Milwaukee",
## "University.of.Wyoming", "Upper.Iowa.University", "Ursinus.College",
## "Ursuline.College", "Valparaiso.University", "Vanderbilt.University",
## "Villanova.University", "Virginia.State.University", "Virginia.Tech",
## "Virginia.Union.University", "Viterbo.College", "Voorhees.College",
## "Wabash.College", "Wagner.College", "Wake.Forest.University",
## "Walsh.University", "Warren.Wilson.College", "Wartburg.College",
## "Washington.and.Jefferson.College", "Washington.and.Lee.University",
## "Washington.College", "Washington.State.University", "Washington.University",
## "Wayne.State.College", "Waynesburg.College", "Webber.College",
## "Webster.University", "Wentworth.Institute.of.Technology", "Wesleyan.University",
## "West.Chester.University.of.Penn.", "West.Liberty.State.College",
## "West.Virginia.Wesleyan.College", "Western.Carolina.University",
## "Western.Maryland.College", "Western.Michigan.University", "Western.New.England.College",
## "Western.State.College.of.Colorado", "Western.Washington.University",
## "Westfield.State.College", "Westminster.College.MO", "Westmont.College",
## "Wheaton.College.IL", "Westminster.College.PA", "Wheeling.Jesuit.College",
## "Whitman.College", "Whittier.College", "Whitworth.College", "Widener.University",
## "Wilkes.University", "Willamette.University", "William.Woods.University",
## "Wilson.College", "Winona.State.University", "Winthrop.University",
## "Wisconsin.Lutheran.College", "Worcester.Polytechnic.Institute",
## "Worcester.State.College", "Xavier.University", "Xavier.University.of.Louisiana",
## "Yale.University", "York.College.of.Pennsylvania"), class = "data.frame"))
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -7281.68 -1275.45 88.13 1314.46 7118.31
##
## (Dispersion Parameter for gaussian family taken to be 3958862)
##
## Null Deviance: 9568659608 on 583 degrees of freedom
## Residual Deviance: 2177372513 on 549.9996 degrees of freedom
## AIC: 10564.11
##
## Number of Local Scoring Iterations: 3
##
## Anova for Parametric Effects
## Df Sum Sq Mean Sq F value Pr(>F)
## s(perc.alumni, df = 3) 1 2277943244 2277943244 575.4035 < 2.2e-16 ***
## s(PhD, df = 3) 1 377458006 377458006 95.3451 < 2.2e-16 ***
## s(Grad.Rate, df = 3) 1 737317805 737317805 186.2449 < 2.2e-16 ***
## s(Top25perc, df = 3) 1 41801474 41801474 10.5590 0.001227 **
## s(Books, df = 3) 1 1615073 1615073 0.4080 0.523271
## s(S.F.Ratio, df = 3) 1 481006425 481006425 121.5012 < 2.2e-16 ***
## s(P.Undergrad, df = 3) 1 38364658 38364658 9.6908 0.001948 **
## s(Enroll, df = 3) 1 178866843 178866843 45.1814 4.503e-11 ***
## s(Accept, df = 3) 1 426427233 426427233 107.7146 < 2.2e-16 ***
## s(Apps, df = 3) 1 31963476 31963476 8.0739 0.004657 **
## s(Expend, df = 3) 1 1138460948 1138460948 287.5728 < 2.2e-16 ***
## Residuals 550 2177372513 3958862
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Anova for Nonparametric Effects
## Npar Df Npar F Pr(F)
## (Intercept)
## s(perc.alumni, df = 3) 2 4.020 0.018479 *
## s(PhD, df = 3) 2 2.144 0.118148
## s(Grad.Rate, df = 3) 2 6.275 0.002020 **
## s(Top25perc, df = 3) 2 1.051 0.350229
## s(Books, df = 3) 2 4.458 0.012007 *
## s(S.F.Ratio, df = 3) 2 10.142 4.723e-05 ***
## s(P.Undergrad, df = 3) 2 1.598 0.203225
## s(Enroll, df = 3) 2 11.026 2.019e-05 ***
## s(Accept, df = 3) 2 9.406 9.627e-05 ***
## s(Apps, df = 3) 2 5.346 0.005018 **
## s(Expend, df = 3) 2 66.784 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1perc.alumi, Grad.Rate, Books, S.F.Ratio, Enroll, Accept, Apps, and Expend show strong evidence of a non-linear relationship with the response variable, Outstate. We are able to detect this non-linear relationship by looks at the small p-values in the ANOVA for Nonparametric Effects Table.